I might add to all the suggestions about driving in our congested island and mention the usefulness of the  'Park and Ride' Car Parks which are found on the outskirts of most of our towns and cities. These enable the motorist to park on the outskirts of the town and take a bus into the centre. This is a much easier and cheaper option than trying to park in the centre of say, Oxford or Bath. It is often more pleasant to explore such towns and cities on foot. Oxford is an excellent example, much of the city centre is inaccessible by car and nothing can beat walking through the ancient cobbled lanes between the colleges and catching a view which has changed little since medieval times.

 http://www.oxfordshire.gov.uk/cms/public-site/park-and-ride

Most other major towns and cities in England have similar schemes.  

Thanks Edward and James for the useful information.  The walk between the colleges sounds wonderful; is Christchurch in that area?  And might either of you know of a good spot near there for dinner? 

Also, we are staying several nights near Amersham, do you know if that tube station is a good option into London?

All the old colleges of Oxford are in an easily walkable area. Many of the colleges, including Christchurch,  are open to visitors for a small entrance fee. Oxford has many restaurants and pubs, so whatever your taste in food, you should find a suitable eating-place.....Maybe Ron, being more local to Oxford than I am, has some suggestions?..

The journey from Amersham to London should be fine by tube, but will be quite busy at commuting times.