I've eventually found some "brake grease", which wasn't as easy as I thought it would be. (Well, I found some on ebay, but baulked at paying £5 for 5 grammes). Every motor parts shop I went in knew what I meant, but didn't sell it. I eventually ended up in a place which looked like it hadn't changed much since about 1962 - an old cellar in a Victorian warehouse in Hinckley (yes, that Hinckley - I work near the Triumph factory).
It cost 50 pence for a small satchet, so I've bought a few satchets and will be giving it a go some time in the next few days - I'll let you know if it makes any difference.