I have been having a bit of a mess round with a Webley Junior the last few days,repaired/ put together a couple last year and have recently by Pm and phone call helped someone sort one out. I thought I'd post up a few things about them here. Here is a diagram of the later Mk2 version, with the alloy body and a stirrup catch instead of the sliding catch like on the Mk1.
https://www.gunspares.co.uk/products...-Pistol-MK-II/

As you can see, there are very few parts in the pistol. The trouble is, with neglect you can get multiple problems. If a pistol becomes "slow" to cock or wont cock at all, it could have various reasons why. Assuming a new mainspring has not been fitted, then it could be the sear, piston,worn long link or a worn small link. In my limited experience of Webley pistols it is usually the small link (BK119) that has worn-----and bear in mind, the Mk1 version of the pistol is at least 50 years old and could be 90!
Anyhow---what can happen is the front of the small link wears and it will barely pull the piston back far enough to engage properly with the sear. This causes the flat holding face of the piston to wear rounded and also the sear. As it becomes more difficult to cock the gun, Mr Chimpanzee uses more force to cock it ("You just need the knack") and the problem gets worse and worse. It can result in a knackered piston and sear.
If you have a gun that is not cocking, it really helps if you have another you can swap bits over from. To save you trying to remove the pins on the cocking linkage, that might not need removing, it helps if you have the barrel and linkage off a working gun to swap over to try.
The pistol I was helping someone with via PM and phone turned out to have the worn small link, the holding face of the piston was rounded but was cleaned up in a lathe, the sear was knackered AND the mainspring it had was too long.
So----Have a think when your Webley starts to become difficult to cock----and try to avoid an expensive job.