There is a fair amount of (mostly free) wifi in shopping centres, cafes, libraries, etc, in cities and towns. More rural areas (villages etc) may be more of a problem.
The mobile phone network "Three" will sell you a mobile broadband dongle for your laptop (if you have access to one) for £30 including 1GB of data valid for 30 days (or £40 including 3GB). Coverage is pretty good in my experience (I use it as my main Internet connection at home and out and about), but again I haven't tried it in rural areas. It does save hunting around for a wifi spot, though, and often seems to have better coverage than the wifi on some coach and train services.
Other networks also offer mobile broadband, but I think Three probably offers the best deal (but deals vary, so feel free to check).
If you have unlocked quad-band GSM (3G, preferably) Internet-capable phones, you might want to investigate getting local SIMs for them.
Anthony