I changed the barrel on my UK BSA from .22 to .177. I don't know about the newer BSA but it was just a matter of the pivot screw being removed. T.W. Chambers - UK Source is where I purchased my .177 barrel. They have schematics on their web site.
Is your gun a fixed barrel or a break barrel? Barrel swapping is much easier on a break barrel.
You might be able to tap the pivot out with a hammer and drift. I've done it on a Webley Vulcan and it was easy. You'll also need to swap the linkage unless your new barrel comes with it. You just need to replace the linkage rivet unless you can reflare it after removing it.