So far, I've booked a flat in London:  "Russell Square Room with a View" courtesy of Airbnb, a super site that puts you in touch with people who have rooms, apartments, houses to rent.  Here's the description:

"Enjoy our cosy room in an artistic family flat- surprisingly quiet at night. Lovely breakfasts served on hand-painted china -espresso or tea to wake up to. A very central location served by Holborn and Russell Square tube Piccadilly and Central line. Be down in Soho or Covent Garden 15 minutes by walking...or 38 and 19 bus. Carry on to Green Park and walk through the park to visit Buckingham Palace...half hour journey...We have a very mellow rabbit in the living room who will come out and say hello. Ben is nine years old and a Cub Scout who might show you latest Lego creation.
The bed is a fabulously comfortable top quality American Queen sized bed. You will get a good night's sleep here.
Guests have access to the bathroom with its London tube map shower curtain. Towels and linens are provided. Toiletries are provided if needed.
Access to kitchen. Feel free to cook your own meals if you wish. Or sit back and let me make you breakfast. Drawer and hanging space in bedroom. Your own key to come and go as you please.

It's like a small village in the centre of London. Bloomsbury...home of Virginia Woolf, Charles Dickens and WIlliam Morris. Cosy cafes and restaurants. A clean, safe, tidy neighbourhood with easy access to most of London's central museums and fun places..."

What sold me was the queen-sized bed.  I've discovered that it's not easy to find a room to rent with a bed bigger than a regular double. 

I've communicated with Joanne and she assures me I'll have room in a kitchen cupboard & refrigerator for any foodstuffs.  We're planning to have a good breakfast at the flat, a nice dinner out in the afternoon and then a soup, sandwich, salad, something light in the evening.

Not staying a hotel allows us to cook and save money from having to eat all our meals out.  Gives us an opportunity to spend money AT THE DOCTOR WHO STORE!!!!! oh yeah.

I'm unable to copy a photo of the house, but here's the listing with access to photos.  All in all, sounds like a great way to start our great adventure!
https://www.airbnb.com/rooms/223498