Island2Dweller

The train ride is just short of 90 minutes. Entirely doable. Cheaper tickets (called "advance", which is a particular fare type) will be available about 10/12 weeks before travel date. These can be as low as £15 if you book as soon as the "advance" fares are released. The exact release date for these tickets isn't an exact science, but keep checking around that window. The "advance" ticket is only valid on the train you nominate. Walk up fares on the day are also available, are valid on any train* but will cost more. Between £40 and £55 (varies between weekday rush hour or off-peak. *Off-peak tickets can be used on any train except weekday rush hour)

As others have noted, you have multiple tube routes, all will work. I would choose to walk across the river (using Hungerford Bridge) to Embankment station. The District/Circle line from there to Tower uses bigger trains and they are air conditioned, so even if busy they're not as claustrophobis as the traditional tube type train.

You can buy an Oyster if you want (each card costs £7, not refundable) but Oyster is no longer the dominant payment method. Contactless (bank card. smartphone, smartwatch) is now the usual payment method, has no upfront fee, and can be used to more destinations than Oyster.

It wouldn't have made any difference where you were sitting. You landed on an easterly approach, which means you did not fly over central London at all. Most approaches are westerly approach, which does go over central London. But it all depends on the wind. About a quater to a third of the time, they fly the easyerly approach

What's your attitude to risk, and do you have travel insurance that will cover missing the flight? You "should" be able to make a flight at 1300, but you have a number of risk factors. Your ship should dock by 0800 but that is not guaranteed, occasionally vessels dock late. Your transfer uses some of the most congested roads in Europe, and even a small shunt can cause massive queues. Booking your own flight means you carry all the risk if that flight changes. Airlines do retime flights, and might move it forward. A more frequent occurence than you might imagine. All quite small risks, but the cost of missing that flight is presumably very high... All down to risk appetite

The trick is to avoid the height of the morning rush hour. If you took the 1028 train out of Southampton, you'll be in Waterloo before noon. You'll have no problem with bags at that time of day.

It's less than a hundred miles from Geneva to Lyon. No flights, but lots of trains

You can buy the rail tickets at London Bridge (mainline station, not underground station). Then use them on the train (towards Charing Cross) one stop from London Bridge to Waterloo East, which is linked to the main Waterloo station. Your ticket will be from "London Terminals" which means it is valid from London Bridge, you don't need to pay separately for the ride to Waterloo. No advantage in buying in advance and unlikely to be any queue to buy at the ticket office in London Bridge at a weekend. Why does the ticket booking engine show the expensive "anytime" fare for a weekend when you never need to pay that fare? Oh - you could write a doctoral thesis on the complexity of UK rail fares combined with the idiocy of whichever sixteen year old programmed the ticket buying sites.

The train from Waterloo goes to Riverside, not W&E Central. Whether is the best option depends where you will be staying in Central London, If it's somewhere near Waterloo / South Bank then this is a good option. If elsewhere, using the Elizabeth Line to Slough then switching to the shuttle train into W&E Central is better. If you use the line to Riverside, you need a traditional paper/card ticket. Buy on the day, either from ticket office or machine. If you use the Elizabeth line option, don't buy a physical ticket, just use contactless bank card (or phone or smartwatch).

National Express do run to Victoria coach station. That's not especially handy for either of the hotels you mention. If you want the fast and cheap option, use the underground (tube). One change needed (same platform / 2 yards walk). The stations you would use for either of these hotels have lifts, so easy with luggage.

If you mean "seeing all of the Tower" in one day, yes that's entirely feasible. If you mean "all of London", no - not a chance. A month might do

You can do it by train. A "walk up" flexible "off peak single" ticket (valid after morning rush hour is over) costs only £27. The downside is that it takes two and a half hours and requires two changes. Train to Redhill - change - train to Tonbridge - change - train to Dover. I'd be quite happy with that journey, but I routinely use public transport just about anywhere in the world. You'll have no problem getting a seat. There is also a train route with only one change (at London St Pancras) but it costs about twice as much and isn't faster. Using National Express coach for this journey isn't feasible. Private Hire pre-booked car service will be quicker but cost a lot more. A taxi off the rank at Gatwick is also possible, but will cost more again.

National Express coach goes to Victoria coach station. A couple of miles from Charing Cross, so not particularly handy fo your hotel. Cheapest (and often fastest) is by underground (tube). Will take under and hour and cost less than £6 per head (so long as you use a contactless bank card / smartphone / smartwatch). Piccadilly line from Heathrow (the trains start at the airport so you will always get a seat). Change at Hammersmith (cross platform, about 2 yards walk) to District line to Embankment. Five minute walk to hotel. Perfectly safe, at your time of day it won't be too busy. Not recomended on a very hot day as not air con. Convenient option is a pre-booked private hire car. Many options such as Blackberry and Simply Airports. The driver will meet you at the arrivals door. Price is agreed and fixed in advance. Comfortable but costs much more than the tube.

Safest? London is (by international standards) an incredibly safe city. Just use usual "big city street smarts" and you will be fine. The train/DLR combination is perfectly safe if you prefer speed and value. A pre-booked private hire car is definitely simple, but won't be quicker and will cost a lot more than public transport.

I don't think Heathrow is any less busy on a Sunday. If everything works like clockwork, you should make it, but you have zero contingency for any hiccups. I would want to have a pre booked private hire car waiting. As mentioned above, there is no guarantee that any Uber driver would want to accept this trip. Furthermore, if you use Uber, you have to make your own way to the designated car park (where Uber drivers have to wait), whereas a Private Hire driver will meet you at the arrivals door.

The Eastern flight can be bought as a through Air France itinerary, they do interline

If you want to fly into Southampton from the US you don't have many options. You need to look at KLM (changing in Amsterdam) or Air France (changing in Paris). You need to weigh up the ease of using Southampton with the extra hassle of a transfer at either AMS or CDG.

I understand the sentiment. But just to alert you to how life in London has changed. Plenty of places in central London (bars/cafes/restaurants) are now card only. Bring cash and you will be politely turned away.

I'm slightly puzzled by the number of posters on this forum who seem convinced that taking their credit card out of their wallet will cause them to lose it. Use of cards (or smartphone or smartwatch) is now the dominant payment method for travel in London and it works just fine for millions of folk here. You can still buy an oyster card if you wish, but that has a £7 (non refundable) upfront fee and is valid to fewer destinations than bank card.

The Novotel is literally at the door of Greenwich railway station. It's also only a five to ten minute walk to the historic core with the naval college etc. It's also connected to the DLR network. Using that you can make one change (at West India Quay) to then get the Elizabeth line to Heathrow. If you book an "advance" rail ticket, (it's a particular ticket type, it is valid on the booked train only) you can get four people from Southampton to Greenwich for about £75. You can buy "walk up" tickets on the day, but that will cost about £130 for four. You would change at Waterloo and London Bridge, which sounds daunting but is not as hard as it sounds. Escalators and lifts available, so you don't need to haul bags up stairs. A car service is obviously door to door convenient but will cost much more. Traffic is unpredictable. About once per month (very rough average) a problem with the Blackwall tunnel will cause Greenwich to go into gridlock. Never any way to predict.

The area is not as busy as the West End, but it's no longer the case that the City is deserted in the evening or weekends. The Bank/Tower location is ridiculously well connected for tubes and buses. As mentioned above, rooms in Hub locations are very small, and if you have large luggage that can be an issue.

Indeed, you're correct. They've changed the rules again. It used to be that the purchase charge became credit after a year. But now the £7 for a new card is now is never refundable. All the more reason to do as most folk in London do and use a bank card / phone or watch instead, rather than buy an oyster. Additionally, oyster is valid to fewer destinations than card/watch/phone.

If you decide to use the train, but don't fancy walking back from the station to your ship, get off at Grays. That's the stop before Tilbury. There will be taxis waiting there, whereas you won't get one at Tilbury. There are also more trains from London to Grays than to Tilbury.

Yes, you can get a refund on the cash balance, but you don't get the £7 that it costs to purchase the card back. (After 12 months, that £7 becomes available as travel credit, but not before).

Oyster was innovative when it was introduced two decades ago, but it is now "old tech". It still works, but it is no longer the most used payment method in London. A contactless (wave pay) bank card or smartwatch / smartphone is all you need, and cheaper because it avoids the non-refundable £7 that oyster costs. You mentioned "find tube" but depending on the precise location of your hotel, the new Elizabeth line may be better. Slightly more expensive but much quicker, much bigger and more comfortable carriages. And air conditioned.