London is a big place and if you can avoid driving, avoid it. Walk as much as possible and take transit as much as possible.
With that said, Alison's place is a more than suitable home base for visitors looking to take in the sights. Nothing was ever more than a 2 mile walk or a single-transfer on transit. To/From Gatwick/Heathrow, take the Victoria line to Pimlico and exit on Rampayne St and walk the short distance to her place.
We were able to visit so much on foot/transit/Uber/pedicab: Lyceum Theatre, Mercato Metropolitano, Millenium Bridge, Buckingham Palace, British Museum, National Gallery, Tate Britain, Tate Modern, Borough's Market, Trafalgar Square, Westminster Abbey, London Eye, Parliament Square, Oxford St, etc.
The neighborhood is nice and quiet with the occasional sound of coppers going by on horseback but don't let that fool you, London does not sleep and the locals still get a bit rowdy at all hours of the night :P
Alison is super welcoming, accommodating, responsive and helpful. The wifi is strong, the place is clean, she even had an outlet adapter in the room for travelers, she leaves you a drawer/shelf in the fridge and so on.
If we get the chance to head back, we will definitely make certain to stay with her again.