Interesting. The ability to charge a late fee is guaranteed by the Late Payment of Commercial Debts (Interest) Act 1998 which sets the statutory rate. Even though you could set significantly higher rates in your contract, the client might have remedy under the Unfair Contract Terms Act, where the supplier would have to show that the late fee is reasonable in relation to the damages sustained by late payment. Late payment is a breach of contract, so late fees have to be in line with the actual damages caused by that breach.