I feel the need to educate
There has never (in the last 30+ years or so) been a right to cancel a services contract after it has been performed. Any cooling off period or cancellation rights exist only up until work starts. Any waiver signed, has the effect of confirming that cancellation rights end given work has started, you can't waive statutory rights. Further if you cancel you still may be liable for costs incurred up to that point, subject to agreed terms. The cancellation rights being discussed in this thread, are largely related to distance selling and contracts formed in the home (or consumers place of work).
Cancelling goods and services:
Prior to The Consumer Contracts (Information, Cancellation and Additional Charges) Regulations 2013, we had The Consumer Protection (Distance Selling) Regulations 2000, which replaced The Mail Order Transactions (Information) Order 1976. We also have the Consumer Rights Act 2015
http://www.legislation.gov.uk/ukpga/2015/15/contents/enacted None give you the right to change your mind for services after work has been completed.
We also have (but not applicable here)
The Cancellation of Contracts made in a Consumer’s Home or Place of Work etc. Regulations 2008
https://www.legislation.gov.uk/uksi/2008/1816/regulation/1/made
and for completeness the Consumer Credit Act 1974 (as amended)
The OPs situation is covered by basic contract law. if as reported, no price was discussed or agreed, then the OP's mrs was not under any obligation to pay the demanded price and could have haggled a more reasonable deal. She entered in to a contract when he presented the bill and she paid the bill. Up until that point the fee (the consideration) of the contract had not been agreed, so the contract was incomplete. The locksmith was to some degree working at his risk, until she agreed to pay. The necessary components are offer to do something for consideration (an agreed fee in this case) and acceptance by the other party.
