Noisy Radiators - No room for pipe expansion?

Hi, You're problem is not unique at all, it often happens as a result of a large job such as a heating overhaul or new bathroom install, the pipes pass through & over joists and are often clamped down by the overlying floorboards. In-fact there are so many possibilities.... It may sound like the noise is at the radiator but noises transmit around a whole system which makes location difficult . If you're going to attempt to clear around the pipe into the floor, be careful of the tile breaking where you don't want it to, that you don't damage the pipe or fittings & definitely wear safety glasses in-case a shard of tile fires off towards your eyes. You could try proving a point at the floor junction by spraying some silicone spray around the hole to see if that helps. I would probably start at the boiler circulating pipes, on the flow side where it's hottest,quickest & try a process of elimination around the system. This can be difficult to remedy though, if it's covered by flooring. If you were to consult with a local plumber it may be that the introduction of some plastic pipework somewhere in the sytem, that you can access might just allow the expansion to happen within that or even if it just eases it to a bearable level. Good luck