london, then 8 days - where?

Train service is good to York and Edinburgh, and you might save some time by flying home from Edinburgh or Glasgow if your flights aren't already locked in. Those two cities (maybe Glasgow too) could keep you busy for the days you have after London.

Hadrian's Wall is wonderful for hiking or just visiting (we liked Housesteads and Vindolanda), and a bus (AD 322 I think it's called) runs along its length so you don't need to drive. You could get a train to Newcastle (also with worthwhile sights though I haven't been there). Another nearby city we enjoyed a lot is Durham. The Lake District is somewhat west of the London-York-Durham-Newcastle-Edinburgh line and might be harder to get to without your own wheels.

Don't try to "do" too much in those 9 days, pick two or three places and give them adequate time. York is easily worth two full days, or three. Edinburgh more. And you could always add time to your London week. Have fun planning!

Edinburgh will involve some travel time, so factor that in to your number of days on the ground to do things, after London.
If you're up that far north, you might as well see Hadrian's Wall. And the Lake District. You can see York on your way up or your way down. That should take up the 9 days. If it doesn't, you can see northern Wales.

The trains don't run everywhere in the country, so you may need to interface with the bus system, add extra travel time for that.

(Edit: I didn't see the 1st post until after I'd written this.)

53,

i took a bus tour up to Loch Ness. It was more or less and all day tour from Edinburgh.

Happy trails.

It's very easy to get from London to York via train. I would spend 2 nights there and then head on to the Lake District for a taste of the English countryside since by then you will have then seen two cities. If you stay for 3 or 4 nights then you can get a good overview and see the highlights. It's easy to get to the Lakes by train from York to Manchester then Oxenholme, and then the public bus system, once there, is very good. If you are avid walkers then you will love the Lakes! There is history as well as walking and it's just downright beautiful as well.
After that, Edinburgh is not far by train - you can take the bus from Keswick (in the north part of the Lakes; this is where we usually base ourselves) to Penrith and then it's just a few hours on the train. That gives you time for 3 or 4 days in Edinburgh before heading back to London.

This article by Rick Steves may help you plan your journey. Great Britain Rail Passes:
http://www.ricksteves.com/travel-tips/transportation/trains/britain-rail-passes
You have already received some excellent suggestions.

You can find something interesting in England by going in any direction from London. To the south is the county of Kent, which has many lovely country houses, gardens, and castles to see. Leeds Castle was one of the castles Henry the 8th remodeled. Hever Castle was home to Anne Boleyn and her family. To the southeast of London are Canterbury with its historic cathedral, and Dover Castle that overlooks the sea.

To the west of London, you could spend some time in the Cotswolds cute villages, go to Bath, see Stonehenge and Avebury. Then see Stratford-Upon-Avon and Warwick Castle.

When you finish your trip to York, Hadrian's Wall, Edinburgh, and a day in the Lake District, you could come full circle and come down into the Cotswolds and do a few of the things near there I mentioned. If you finish up in the Cotswolds, it's an easy trip back to London by train.

You will be only two hours and 25 minutes from the heart of Paris via Eurostar. Eurostar tickets go on sale 6 months prior to travel and can be had for around $56 RT. We always fly into LHR, spend a few nights, then Eurostar to Paris and spend maybe 7 nights. If you opt for that, September is a very busy month in Paris and hotel rooms book up quite early, like 6-8 months in advance. Check out www.tripadvisor.com, Paris travel forum, and ask for hotel suggestions. We enjoy both cities and split our 2-3 weeks between them. We too like York, Edinburgh, and the Highlands (grouse hunting) but remain enamored of Paris after 8 trips to both the UK and France.

Thanks everyone! We have homework to do, especially about public transportation and advance ticketing. We are locked into flying in and out of LHR. We especially like the Lake District ideas and also perhaps will check out some day trips out of Edinburgh and explore York up or back. Concentrating on fewer areas makes sense.