It isn't likely to be cost-effective to do this by 'getting someone out' for such a small requirement.
The chemical can be purchased from Wickes for £8 for 500ml (B&Q seem to have stopped selling it, probably because of safety data sheet implications) and you just brush it on, taking appropriate cautions against the fumes.
You need a handyman type person and his labour expectations are going to be driven by the hassle factor, plus the perceived risk. My guess would be £50 for an hour's work, once you've sourced the chemical.
You do not want the house treatment service people, whose overheads include the 10-year warranty-backed insurance policy, for something relatively small and trivial.
European Furniture Beetle (the most common type of woodworm infestation) has a long life-cycle (several years) and takes ages (several decades) to chew structural timber to the point of compromising integrity. If that's what this is. Death Watch Beetle is different.
This is best DIY really - or not at all. It's a shed.