Hotel or Apartment/B&B in London

London is very expensive. I would stick with the free place to sleep. There are plenty of ways you can experience "real" London. Most people consider apartments/B&B because they are cheaper, and will often include a kitchen that can help reduce costs. You can now use the money that you would have spent on lodging on other things while in London.

I agree with Mike, save your money and sleep in comfort. B&Bs can be a great way to meet people, mostly other Americans if you stick with the guidebook-recommended ones. Picking one out of the air can be disappointing, or great, it's a crapshoot. Last year we stayed in seven places over three weeks in England and Scotland, including five B&Bs. They were all fine and memorable, but our best sleeping, in-room laundering, and wifi connecting were in the Radisson Blu hotel in Durham which was offering deep discounts at the time. Your hotel room is mostly for sleeping anyway.
An apartment is a different equation -- again can be full of surprises, but you have room to spread out and a kitchen to save money on meals. But if I were you, especially in mid-August for an October trip, I'd take the bird in the hand. The "real" London will be all around you, and you'll enjoy it more after a good night's sleep!

You will see plenty of 'real' London as you walk around! where you are staying is 'real'- we often stay in that area. Don't fret.

The Doubletree is a "real" hotel in a "real" city. There is a certain group of people who seem to think that the only way to get an authentic experience is to stay in a family-run hotel, B&B, or apartment. While they might provide a different experience, it is no more real than the experience you will have at the Doubletree. The people who work at the Doubletree will live in the London area (they are real people too) and the people who stay at the Doubletree will include all sorts of travelers. I've stayed in many types of hotels in London and also lived there in a flat for a year. Every experience that I had was "real" , even the times that I stayed at the Holiday Inn for free on points :). The good news about using points is that you will have more money to have other "real" experiences in London. And those other experiences (great meals, pubs, theatre, sights) will be far more memorable than where you choose to sleep. Have a great trip.

Free lodging is a plus. Remind the travel partners that although you are visiting one of the best cities on the planet it is also an expensive one. Real London will be ALL around you. For a fun yet practical (if you've been sight seeing around Parliament Square) is to stop for a pint at the Red Lion Pub on Whitehall. It's where Barristers, Government Officials, Parliament members, even a Lord or too enjoy libations. Have listened to and engaged in some very intriguing conversations while sharing a pint or two there. In fact it's become a family tradition to make it our first stop each trip. Same faces. Feels comfortable. The Two Chairmen Public House about 5 blocks from Westminster Abbey is charming and if you look down Queen Anne's Gate you'll see a wonderfully preserved residential street. Imagine Sherlock Holmes. Take the tube to Hampstead and walk into and around the Heath. Londoners will be out and about, with their dogs and families. People will be playing sport. Having lunch. Same scenario is repeated in all of London's lovely parks. Enjoy them.

I have to agree with the others. A hotel is a place to sleep. Being out and about is how you will experience the real city. When I rent apartments it is to save money, have more space, be able to do light cooking (coffee, tea, make some sandwiches, etc.), and have access to a washer without having to spend time at a laundromat. If I had a free place to stay, that is where I would be staying!