Basically yes, in answer to your question, but you’ll be lucky to find someone who won’t want the car brought to them. The seller should be expecting that a serious buyer would want to have a pre-purchase inspection carried out, but it will need to be at the buyer’s expense and inconvenience. Expect to budget in the region of £400 plus transport (there’s the odd one I know of who’s based around the London area who’s mobile, which helps).
As others have said, marque is important as they all have their quirks, and at that age you’ll probably want to strike up a good relationship with a well regarded independent anyway rather than pay main dealer prices for questionably experience (yes, really).
The inspecting garage will have their name and reputation attached to it, so go for someone who has those things, and don’t forget they’re working for you, not the seller, so in their interests to find things wrong with the car that you can negotiate on and then work with them post-purchase to prioritise and sort as time and budget allow.
Don’t look at this as a wasted expense or try to skimp on doing it. It really is the best ££ you can start throwing down the money pit (if you hadn’t realised it was one of those and weren’t relishing the prospect of something to throw your hard earned at then you’re barking up the wrong tree).