I'm visiting the UK and I have about 5 days free which I'd like to spend exploring an area in the English countryside. I'm looking for suggestions for a place to base myself. It needs to be accessible from London by train as I'm travelling alone and don't want to rent a car in London. But I'd like to be able to rent a car to explore the local area when I get to my base. Currently I'm considering Lake District, Cotswalds or Cornwell. I know this is a vague question, but I'm interested in people's suggestions if they know these areas. I don't have a must-see list, I'd just like to roam and take in the sights.

It depends on the time of year.

If you are going in July or August, the Lakes, Cotswolds and Cornwall will be heaving. I'd only visit when there is an "R" in the month.
Out of season, would be much better.
For example, the weather in Cornwall is still pretty mild around October.

As an alternative, you could consider Yorkshire, East Anglia or the Peak District.
They don't get the great crowds of foreign tourists.

I think that in your place, I'd take a train to Bury-st-Edmunds.
It's a nice town in its own right and you could hire a car and visit places like Lavenham, Southwold and some of the Suffolk villages.

Have a look at some of my photos of the area at http://sylvia.photoblog.me.uk/c1250171_1.html


and http://sylvia.photoblog.me.uk/c450498.html
It's a beautiful area.

Your short list - Lake District, Cotswolds, Cornwall is predictable. You don't say when you are going, but can I suggest a couple of other options far less touristy?

Durham, for the cathedral, North Yorks, Hadrians Wall. Northumberland in general.

Poole or Dorchester for glorious Dorset. And Somerset.

But don't plug yourself into having to return to the same place every night. If you have wheels you can move around.

North for majestic landscapes (can be bleak but all the better for it). Or south for sunken lanes, thatched cottages and a network of tiny roads to die for.

Yorkshire has just won a Prettiest county award so worth visiting. Trains easily get you to York or Leeds which are the most obvious city centres for such a tour. The counties (there are 4 yorkshires) abound with rental accomodation

My suggestion would be Yorkshire Dales and Moors or Northumberland. Breathtakingly beautiful with so much to see and do. I've been to nearly each area in England and the north is by far my favourite. Absolutely stunning.

Follow Hadrian's Wall.

I would definitely recommend North Yorkshire, basing yourself in York and not Leeds. I work in Leeds, which is a big, busy industrial city, not really a tourist place (although the shopping is terrific.)
London to York is quicker by train than London to Leeds, and York is a beautiful city to stay in with much to see. Alternatively you could pick up your rental car in York and base yourself somewhere smaller, but definitely do spend some time exploring York itself before heading to the countryside (you won't need a car when in the city itself as it is very compact).
Using York as a base you have access to two stunning and very different areas - the Yorkshire Dales and the North Yorkshire Moors. Coastal places such as Whitby, Staithes and Robin Hood's Bay are also great.
With a car you might like to stay in farm or rural bed and breakfasts. These are often very good value, and I get the impression you would like to stay deep in the countryside. This website gives you lots of rural bed and breakfast places in the area.
www.yorkshirenet.co.uk
I live in North Yorkshire and could easily give you ideas to fill 5 weeks, let alone 5 days! It's such a beautiful area with gorgeous countryside, friendly people, great food etc etc. Even in the summer you can avoid the crowds with a bit of careful planning. Major highlights, as well as the ones mentioned above, are Fountains Abbey, Castle Howard and the NY Moors Railway. Here are some links to help you
www.visityork.org
www.yorkshiredales.org.uk
www.yorkshiremoors.co.uk
www.nymr.co.uk
If N Yorkshire appeals and you'd like some more help please don't hesitate to give me a yell and I'll do my best to assist.

Second Morgana - I should have specified North Yorkshire.

Morgana

How about Kirkby Lonsdale - its on the up full of good cafes/home interior shops and is very well placed for an international tourist.

The Lakes/North Yorks/The Dales and Northumbria are all pretty doable in a day.

Its also nearly in Lancashire which makes it nearly perfect!

I agree with the above about N Yorkshire being a great place to visit however do not walk away from Leeds as an alternative centre. It makes visiting the Bronte Centre very easy. The Unesco WH Centre in Saltaire is also very easy while Leeds offers not just great shopping and dining but good theatre etc for nice evenings.

Many thanks to everyone for their ideas. You have given me some areas to consider that I hadn't even thought of, so I'll enjoy doing some more research. I'll be travelling in September, so I should miss the worst of the summer crowds. Thanks again for the help.

Around Dorchester would be great, especially if you enjoy walking. There are also very attractive rail routes from Dorchester. If you go there, read up on Thomas Hardy. You would be able to visit the Jurassic Coast, Lyme Regis, Weymouth & Portland, Salisbury & Stonehenge, Maiden Castle, Lulworth Cove, Poole Harbour & Brownsea Island, Arne & Corfe Castle, Glastonbury, Sherbourne and Shaftsbury.

The Lake District and the Peak District are two of my favourites. The weather may be slightly better in the Cotswolds or Cornwall. All are lovely.