I don't own a shredder, so I never shred my old bank and credit card statements. I don't own an underground nuclear bunker either, yet here I am anyway. Instead, I dilligently keep all bank communicaes for a period of no more than fourty-five seconds, before they get torn into no more than two pieces, and tossed into no more than one kitchen bin.
When I first heard about this bank charge thingymebob, I was initially concerned that not spending the last six years catologuing every single one of my bank statements into a sensible shoe box, was going to make it all rather difficult for me.
It turns out all that information is easily accesible though. Legally, your bank has to keep all your old statements under the Data Protection Act. It is your right to request them to reproduce it for you. They can charge a fee for this, but this fee cannot excede £10. They are also allowed to take up to 40 days, but are otherwise legally bound to produce, Exhibits A through Z, against themselves.
The DPA, what a funky law for scatty people!

The site Rod has linked to is a good one. They even have an example letter for the Data Protection requests. The meatier letters where you actually demand your money back, I can personally vouch that they do get results. Between the missus and myself, we're better off to a four figured degree for having done all this.
For anyone like me, who was a little irresponsible with their spending habits in younger times, it's well worth the hour or so effort it takes.