It's probably best to use the one where the firm is based, since their local TS department will coordinate complaints about them. In practice though, most local authorities require complaints to be submitted via the Citizens Advice Consumer Service on 03454 04 05 06 (and they'll forward the information to the most appropriate people).
https://www.tradingstandards.uk/consumers/support-advice
Remember though that many Trading Standards departments actually consist of fewer than five people, who're tasked with dealing with all relevant issues across an entire county. They tend to focus on rogue traders who're consistently flouting the law, rather than having much time for individual complaints about traders who're generally causing no problems.
If you require further advice about resolving a specific problem, please give us the details.