Keep P60s/P45s for ever right back to your first job, and if you're ever missing any, then keep the payslips for those employments. Best to keep payslips for the last, say, 3 years. It means that if, as happens far too often, the DWP/HMRC have incomplete history for things like state pension/nic contributions, you can prove to them you paid NIC and were working etc.
For "capital assets" like cars, caravans, your home, home improvements, large items of equipment like fridges/washing machines, etc keep the paperwork at least until you sell/scrap the asset and a couple of years beyond. You never know what you may need, especially during the sale of your home when the buyers/their solicitors will want all kinds of things re the house such as guarantees/certificates for new roof, replacement windows, planning permissions and building regulation certificates, etc. Also, if you have no plans to do, but end up renting out your home, part of the "gain" when you finally sell comes into CGT territory and then you need records of the costs of purchase, costs of improvements, etc. With fridges/washing machines etc and other big ticket items, you may need "proof of purchase" to invoke guarantees/warranties etc but also in subsequent years if there's ever a recall or legal case re faulty goods long after the warranty/guarantee period. Likewise keep motor car repair/servicing bills/MOT certificates, original purchase invoice, etc as long as you own the car - it may help to "prove" full service history to get a better part exchange value.
Bank statements, utility bills, etc., it makes sense to keep 2/3 years. Then "weed" and only keep them if they show something significant, like a bank statement showing a divorce settlement payout or an insurance claim, etc just to have "evidence" of the big/unusual transactions. Likewise, keep the utility bills immediately before/after a switch of provider just in case the meter readings etc are challenged or the utility firm make an error. Again, just keep 2/3 years until you're sure there's no problem.
I'm a big advocate for "weeding" as the years pass rather than having a hard "cut off" of chucking everything out after x number of years. Far better to "weed" out the trivial stuff and just keep the "big" stuff, so you may have a full box file for last year, but only a small envelope for 10 years ago, etc. Each year, look in the file/envelope for that year and "weed out" the stuff that's become irrelevant.