Every region/sub-region has it's own brewers, and believe it or not, but many UK beers do not travel well, so you'll often find that beers are local. I'm not a big fan of the large brewers (e.g., Tetley, Bass, John Smith, Wells, Youngs, Fullers, and Theakstons since they got taken over) as I find the beers very watery and tasteless. I tend to prefer small breweries as I think the flavours are much better developed. There are so many different types of beers - bitters, stouts, porters, IPAs, milds, lagers etc, so it all depends on what you like.
If you can, find a CAMRA listed pub (Campaign for Real Ale) http://www.camra.org.uk/ or better still a local beer festival. If you can find a pub that serves non-pressurized cask ales, then try one, because you'll either absolutely love it or loathe it. I happen to love it - slightly warm, not much fizz, but the flavours come charging through and it's a truly amazing experience. Cambridge has a fair few pubs serving these types of beers.
My favourite UK beers include:
Timothy Taylor Landlord (gorgeous).
Adnams Broadside.
Woodfordes Norfolk Wherry (a multiple award winning bitter, and rightly so) and their dark ale, Nelsons Revenge, is pretty good too.
Hall and Woodhouse Badgers Golden Champion (I've never found it on tap, but it's good in the bottles).
Greene King Abbott Ale.
I love ciders, but I find most of the US "hard ciders" are just way way too sweet, and I hate Strongbow for the very same reason. I like Symonds Scrumpy Jack, a sparkling cider that is fairly dry but has a big hit of apples and is available in many pubs. I've fairly recently discovered Crispin cider imported into the US - the stuff in the cans is pretty good, but the bottled ones are way too sweet for me. You can also try real scrumpy cider, flat, slightly cloudy with an amazing taste. However, I will not be held responsible for any hangovers you may incur - you have been warned
Have fun and I'm very jealous. I was hoping to get back to the UK for Christmas/New Year this year to visit family and friends (and pubs too!), but alas the boss and work has got in the way (again)