Driving in England isn't that bad once you get used to it...my suggestion is to spend some time in a cab first for the purpose of getting a feel for navigating corners, curbs, pedestrians, cross-traffic from the "wrong" side of the road. You can also ask questions of the cabbie. It's easier to drive if you've been a passenger first! I did this the first time I drove in England and it really helped - worth every cent!
1. Renting a car from central London would be easier on a Sunday - much less traffic, especially early in the morning. Do be prepared to pay the extra congestion charge that is applied for anyone driving in central London. You pay through the rental car agency. If you have someone with you who can help to navigate from the passenger seat, that would be ideal. The streets of London are fairly well-marked but there is a lot going on visually so it's easy to miss signs, especially when you're trying to concentrate on driving on the opposite side!
2. This would absolutely be my preference if it were me and I was leaving London on a Sunday. Heathrow is fairly far outside of town and from there it's easy to navigate the motorways away from London and up to Oxford and the Costwolds. It'll take you about an hour or so to get there. Take the Picadilly Line out to Heathrow (about 45 minute ride) and rent a car. Then just hop onto the M25 and then the A40 all the way. It's a fairly straight shot and very well-marked.
3. You actually CAN rent a car on Sunday in Oxford...the Botley branch of Enterprise is open from 11 - 4 on Sundays. We've used this very branch before - it's on the outskirts of town to the west - just the direction you're headed in. But if you can get there on a Saturday then by all means, do that. 4 days in London and 4 in the Cotswolds is a great combination in my opinion! Although driving in Oxford will be no picnic either if you start from a place in town. It's not London but don't expect it to be a drive in the country until you are well out of town. Central Oxford is tight. You can do it though...the Enterprise Rental company in Oxford will even deliver your car to wherever you are staying. You then take the person delivering it back to their office, the perfect opportunity for you to let them drive, get a feel for it, and ask questions before taking the wheel yourself.
4. Not that I know of....but I'm sure someone else on here will have great ideas!
