Another option is
Elizabeth Line -> Tottenham Court Road
Northern LIne -> Charing Cross Station (just two stops, or even walk it)
Charing Cross -> Dover Priory
The first two are a single ticket on TFL (Transport for London); the latter a ticket on
What you run into is the problem with a lot of London Rail. The country is divided (historically) by the railway operators into different slices, and each direction in/out of London tends to use a different London terminus. While some European cities have a 'central' station, London has about a dozen (Waterloo, , Charing Cross, Victoria, Paddington, Marylebone, Euston, St Pancras, Kings Cross, Liverpool St, Fenchurch St, London Bridge....); each serving a different wedge of the country