In English law, a contract can be unwritten, and a contract may in principle be concluded by a handshake or other informal communication.
In the circumstances that you describe there is likely to be an unwritten contract. The first question, then, is: do the terms of that contract permit the customer to cancel the contract and call a halt to the work?
If the contractor expressly agreed with the customer at the time the contract was concluded that there was no right to cancel, then unless statute intervenes there probably is no right to cancel early.
Statutory intervention is most likely to come in the form of the Consumer Contracts (Information, Csncellation and Additional Charges) Regulations 2013, which apply only to B2C contracts not B2B contracts. For a summary of these Regs, see: http://www.which.co.uk/consumer-rights/regulation/consumer-contracts-reg...
It may well be, however, that nothing was specifically agreed regarding contract cancellation at the time the contract was concluded. In that case, absent statutory intervention, it must remain uncertain whether there is a right to cancel (unless a judge decides the issue one way or the other). If standard industry practice allows for contract cancellation, a term to that effect is more likely to be implied into the contract.
In any case, your specific question seems to be whether the contractor is entitled to charge for pre-cancellation work, rather than post-cancellation work. In general, the contractor would usually have a right to charge for pre-cancellation work, although without knowing all the facts I cannot be sure. Indeed, depending upon the facts, the contractor may also be entitled to recover monies in respect of post-cancellation work that was not performed because of the cancellation.
As so often with these Q&A answers, I can't be more specific than that.