If you MUST use grease - and many these days do not - please DON'T use any automotive grease like the stuff you put in bearings. It will make a nigh-on immoveable hard crud on every surface of the gun.
Some use water-pump grease, same deal, it's hydrocarbon based, and therefore very messy to clean up post shoot. Over in the real world, Crisco shortening is THE stuff- makes the air around you smell like a chip van, though. I have no idea what the UK equivalent is, I suspect something like TREX [?]
Anyhwo, here's MY tip, and I've been shooting BP since 1968, so you can bet that if it can be done, I've probably done it. Go into Boots and buy a plastic container of E45 hand cream, and use that.
There are a few reasons why this is a good idea -
1. It is totally water-soluble, and therefore, when you wash off the gun you wash away all the goop with it.
2. It it totally non-allergic [it's a skin cream, right?] - some greases are definitely NOT.
3. It works.
Others may differ- there are, of course, as many answers to this as fleas on a dog.
Keep your automotive grease for the cylinder arbour.
tac