Is there anywhere in Leeds that changes watch batteries cheaply?

The market will have stalls that are cheap.

However your watch, does it have a plain stainless plate at the back. You really need to get a magnifier.

Assuming there are four corners to the plate, under a magnifier you will see that 1 possibly 2 (they will be diagonal to each other) have just the very slightest lip, this is where you need to put a blade to lift it up. A not too sharp knife from the kitchen should do the job, either lever or flip it with the blade under the lip, it is more technique than strength but a little of both helps, and the plate will flick off.

When open there may or may not be a plastic cover, this should just drop into your hand when turned over. The battery is held in place by a tiny thin strip along one edge, but should just come out with a tiny screwdriver and replace with appropriate new battery. when you are putting the plate back try and get the whole level and then press, there will be a click as it goes home, job done.

I used to occasionally sell watches in my Newsagents and learnt the technique there, the Jewellers next door charged £5 plus £3 for the battery, I did a dozen for just over a £1.

There is a watch guy in merion center by morisons by the side entance oppasite yates.