Google a company called Lombard Recycling (based in SE10) and see whether they will collect it from you - assuming you live in SE1, they have vehicles collecting from offices in the area every day and perhaps for a cash sum they will collect it and shred it from you. Otherwise, make a bonfire!
They don't collect from individuals but you can go any time Mon-Fri 8.30-15.30 and take your papers to them.
It's £25 plus VAT (they don't take payment in situ, you leave your address and they invoice you) for "a car load" or, in our case, several panniers full.
You can cycle/drive/walk in to the unit. You tip your confidential waste onto a recessed conveyor belt and off into the shredder then compacter it rolls.
Very satisfying. Very reassuring. Very easy.
The chap asked if we'd had any problems finding them. But we hadn't. There is a map on their site, we have an A-Z, we were on bikes and they are on a bike route.
For SE1-ites, you can use your shredding needs to enjoy a bike ride to Greenwich. You could come straight back, of course, but I'd recommend that, after jettisoning your papers, you continue to the Woolwich ferry, cross to the north bank, then enjoy the mostly traffic-free route back to Tower Bridge...