you need a locksmith, not a joiner. You will need evidence of identity and that you are the householder. You may be secretly photographed.
the AA own a franchise group. Dynolocks, maybe? similar to the name of the drain clearing company.
An ordinary Yale is childs play to open, especially if there is a letterbox in the door, so there should be no need for anyone competent to drill it out, and certainly not to damage the door. Once open, a similar lock can be swapped in, in a matter of minutes.
Since a Yale is so insecure, I'd suggest that you at least have a BS nightlatch fitted as a replacement. Possibly conceal a spare key in the shed, if you have one, or the boot of the car, or with a trusted neighbour.
It's possible that your household insurance covers lost keys, so be sure to keep the receipt. better still, phone them first as they may have a recommended locksmith.