Family History Library
 

... in Salt Lake City, Utah?

https://familysearch.org/locations/saltlakecity-library

Has anyone contacted them directly for them to look up entries please?

My cousin contacted http://www.recordclick.com/ and they put her in contact with a 'professional genealogist' in Salt Lake City, who says that the records for the baptisms for her family in Koblenz are held at the library. However to look them up she will charge several hundred dollars!

Could the records be sent to a local family history centre in London, for example?

Not sure if I've understood you Rachel (got my thick head on tonight) but if the LDS has filmed the record you want, then you can order the film to be sent to any LDS FH centre in the world. This is how I have done the majority of my primary source research. There is a charge of course - £7 I think it is now.

OC

That's what I'm thinking... thanks OC, I'll let her know :)