Can anybody tell me why diesel is leaking out of this part on the engine and whether it might be an expensive fix. This is on a UK Ford focus diesel 1.8 tdci zetec duratorq engine.

 

Welcome to the site..
It's a fuel injector leaking. What year?
I don't have any experience on the 1.8,, also since most of the injector is wet, so hard to know for sure. You might use some brake cleaner and spray it clean/air dry, and ID exactly where the leak is coming.
A single fuel injector wouldn't be a huge cost, certainly a task you or someone handy with basic tools could tackle...

 

Sometimes even after you clean the area , it can be difficult to pinpoint the source of the leak.
What might help is; after you clean and dry the area, dust a little talcum powder over the area and just watch it with the engine running.