My wife and I have decided not to complicate our holiday and have substituted our 2 days in London with 3 in Portsmouth (similar cost) and enjoy a less stressful start to our trip. Portsmouth has a lot to offer and we could always hire a car if we wish to go further afield. We fly into Heathrow on the 26th Sept at 15.40 and plan to book a taxi to our hotel in Portsmouth at a similar cost to using public transport to London and then on to Portsmouth. Good luck with your plans