As one who does the commute, I thought I would go into a bit more detail about how it can work. It isn't ideal, but I don't think it is quite so bad as some people are making out. A lot of it of course depends on the stress of the drive - I note that your dd would have to do a tube ride too, which I think would be the deciding factor of not to go down that route.
DD wakes around 10 to 7, we dress, breakfast and leave the house around 7.35 to drive 3 miles to collect the others, or are collected if it isn't our turn. We do have to drive up to the top of a long track to wait if we are picked up. We arrive on the outskirts of a city around 8ish and it takes another 10/15 mins to get to school and this is the bad traffic bit! Usually the children are in school at 8.20. (starts 8.40). In two years we have never been late, we have been on the nail - but not late.
Pick up is at 3.30 - and for some reason the drive home is quicker and we are usually home by 4.10, this is a similar time to what we got in at our state school, which finished at 3.45 and was only a short 5/10 min drive!
In the car we sing a lot!!! They all have whiteboards to doodle/play hangman etc., and we do times tables to songs. They have been known to read and do homework!! To be honest, they seem to enjoy it, it is a bit of a social and time to unwind.
They could go on the bus, but it leaves at 7.30 from a nearby village - so we would have to leave home earlier than we do now. The return bus doesn't leave school until 4.00pm, as they wait for all the children to come from the Senior schools, so they wouldn't be dropped off until nearly 5pm after the other drop offs, an hour after we get in. Driving therefore is the best option for us.
I know what others are saying about playing with friends locally, but many people who live in a rural area do not have friends next door or down the street and have to drive or make that extra effort to be social. DD goes to Brownies and swimming locally, so does have friends nearby and may bump into them in the supermarket/post office and park, but not on a daily basis, usually we get home play, homework, walk the dogs etc. etc.
Most of her classmates and that of the other children we travel with (one of whom is Yr6), don't have playdates on school nights - is that unusual?