I can strongly recommend staying at Becky’s apartment. It is a 2 minute walk form the Lewisham train/DLR station, which means it is basically in the centre of London. We could get to Westminster or City in 15 minutes anytime in the day (even returning after midnight). The room itself was comfortable and felt quite luxurious.
Most importantly, Becky was an amazing host. We had a really nice chat and she even steamed up some dumplings we had bought earlier.