I generally keep my bills for about 10 years and I have a 4 drawer filing cabinet in the attic in which I keep everything and a very small filin cabinet in the study (tho it used to be in the hall) for stuff I use on a regular basis like passports, birth certs etc.
As for bank statements and credit card statements even some bills now adays, I have all online so I don't get sent them anymore. However some years ago before companies went paperless, my husband spent a long time scanning in important bills and stuff and stored them on a computer. But then again, he is a bit like that and had a very large hard disk on a seperate computer that we were using as a server. (Say no more).
I don't think we need to keep half the paper that we do, frankly, I think all the stuff they send is a waste anyway, what about all the reply envelopes, adverts and glossy information leaflets you get with each bank statement/bill/correspondence etc. Just what do these people think the information superhighway is for???
ANyway, good luck with your move. I hope it goes well.