OFCOM and the ASA banned the use of the word "unlimited" to describe broadband plans with a usage cap, which pretty much killed caps overnight. More recently, they banned "up to" speed claims - the advertised speed must be representative of the actual speed of the majority of users during peak hours. Broadband providers must also offer a guaranteed minimum speed, with the right to cancel the contract without penalty if that speed cannot be achieved.
Especially if you're paying for one of the better services, like Andrews and Arnold etc. They have caps listed on their broadband pages. There have been regular stories where customers have been sent letters about their bandwidth usage even though they're on 'unlimited' plans. The ISPs generally refer to clauses in ToS, which (imho) doesn't mean anything can be 'unlimited'.
I was at Uni around ten years ago (actually it's more like 12, getting old!), I remember we had Sky Broadband (in a flat full of IT students) and seriously abused it. They never complained.