My wife and I just got back from a whirlwind trip to London and it was fantastic! We absolutely loved our short stay in London, and can't wait to go back. We stayed at the Mayfair Townhouse, which was a very beautiful, comfortable, and immaculate hotel in a wonderful location with easy access to the rest of central London; unfortunately the customer service was poor, and the breakfast was alright, so we'll stay somewhere else on our next trip.
Whilst in London, we visited the Tate Modern for a Picasso exhibit, British Museum, strolled around Mayfair and Piccadilly Circus, went to Shepherd Market, and had a private driving tour of various sites in central London, including Westminster Abbey, Trafalgar Square, Buckingham Palace, London Bridge, The Monument, St Pauls Cathedral, and more. We absolutely adored the British Museum; unfortunately we didn't have enough time to see the whole museum, but the exhibits we did see were impressive (Ancient Egypt, Mesopotamia, the Levant, Iran, Nubia, Kush, the Islamic World, Roman Britain, Anglo-Saxon England, Vikings/Norse, Migration Period, and a special exhibit on India). We ate at Hide, Benares, Bentleys, and visited some pubs; all were excellent, especially Bentleys (whelks and cockles for the win!). We tried black pudding, and it was fantastic, absolutely loved it!
Transportation:
Direct flight on Virgin Atlantic from IAD to LHR. Passport control/security at LHR was a breeze. Customs/passport control upon return to IAD was the worst/busiest we've experienced in all our international flights into IAD.
Took London taxis to/from LHR and within London. I wanted to be immersed in the cityscape of London, even if it meant greater expense and time then taking the Tube. We also walked a lot.
Practicalities:
Never used cash, only used credit card and NFC payment apps. London is expensive, but we didn't find it to be too insanely expensive.
For souvenirs we got some tea and chocolates, and a few books at Waterstones; plus lots of pictures.
Next time we go to London we plan on seeing the rest of the British Museum, and go to the National Portrait Gallery, British Library; and an excursion out to Stonehenge and/or the Cotswolds.