What documents do I take to the UK and which do I leave in the US?

We are planning to move to the UK for 2 years or so and will be keeping a US safe deposit box while we are out of the country.  What documents will we need in the UK?  Do we need our Social Security cards when dealing with immigration?
Also how did you get your important files to the UK? I'm not dying to bring luggage full of old paper, nor am I exceited about the prospect of shipping it unattended either.

Will you have someone that can access the files for you if you need something? I don't think you will need to bring much. Your social security numbers mean nothing to UK immigration. I'd bring my old tax returns, birth certificates, any old passports, your driver's license, and maybe any papers related to property ownership. Otherwise I'd scan other documents you might want and have them online.