I was there three years ago and I agree wholeheartedly that you should use public transportation to get around London. You can also get bus day tours to see the sites around London. One day we did this and got to see the Roman Baths at Avon, Stonehenge, and Windsor Castle. I would not want to be locked into a tour the entire trip, but one day wasn't bad.
I will say you will be hard pressed to see England, Scotland, and Ireland in 10 days and have quality time in those places. Our trip was mainly focused on Ireland, so we flew into London, and spent only three days in England, took the train to Wales, took the ferry to Dublin, then rented a car in Ireland and spent the rest of the three weeks in Ireland, and finally flew home out of Dublin. I had driven in Ireland before, so I knew what to expect. Narrow windy roads that barely look big enough for a bicycle in the US, will be a normal two lane road in Ireland. Rent a car with standard transmission for the complete experience!
We were on the go constantly. In Ireland, I think we only stayed at one place (Galway) more than one day. We knew the major destinations we wanted to be near, and booked a few places in advance, but a lot of the trip we left open ended, so we weren't locked in to having to be somewhere. We never had an issue getting a room this way, and it helped pace ourselves. If it was Monday and we were enjoying ourselves in county Kerry we could spend a couple extra days there knowing we don't have to be county Cork until Wednesday.
We stayed at B&Bs most of the time, and had a good experience at most of them. A few I was glad we were only there for a night, but nothing was horrible. We did stay at a hostel in Galway for a couple of nights. It looked brand new so it was very clean, and it was one of the more spacious places we stayed at the entire trip. We even had a private room with a bathroom, and it was a lot cheaper than the B&Bs in the area. So despite the bad rap, hostels can be an option if you're a cheap ass traveler.
As for warm beer, I didn't have one the entire trip. Most of the cask ales in England were served at cellar temperature (around 50 degrees). Every other draft was similar to US in temperature.