It seems what ever gear I’m in the bike wants to change down, particularly under strain. I’ve had a fiddle with the screws on the derailleurs,( and not sure if I made it worse or not) but now not sure if I need a new chain or not. It’s a couple of years old and done a good few thousand K. I can do most things with a bike but the Mechs leave me somewhat blank, should I just take it for a good service?

If so, can someone recommend a honest place in north west Leeds?

Could be very worn.
Have you bent the mech hanger?

I think a pastor could perform the service your chain needs. A few thousand miles ain’t bad, new drivetrain probably needed if its that bad though – chain, cassette, maybe chainrings.

If it ‘needs’ a new chain then it’ll likely need a new cassette and possibly new chain rings (which are often more expensive than a whole new chainset!). You might get a bit more life out of it with a clean, oil and adjustment

Fiddling with the screws is a classic mistake. They are just the stop screws and only affects the mech dropping off the top and bottom. Well that and the b tension screw which affects how close the chain gets to the mech, but just used to adjust smoothness of shifting potentially.

It could have become de-indexed, maybe through wear on the gear cable. Indexing is dealt with via the barrel adjuster(s) at the end of the cable. You could try adjusting this, making small turns and test the shifting. Though it may be you just need a new cable.

Cassette may be worn enough that it’s slipping the chain under load onto another cog. New cassette and chain would be required if that worn.

Why don’t you buy a simple, cheap chain wear checker? It would save you all that worry and probably some expense as well:

http://www.chainreactioncycles.com/kmc-regular-chain-checker/rp-prod120706

Forgot to mention the BB is creaking and clanking as well. Time for a service I think! MTB needs new tyres as well! Bugger.