Worse than that - the CAA says that the information required by the FAA is stored on a computer - and, under UK law, is subject to the Data Protection Act.
They do not have the authority to pass the details to the FAA.
There is also the financial aspect of which you speak....who is going to pay for the time taken for some CAA employee to glance at the computer to verify the information??
Best way to do it would be to take an FAA check ride - you should already be learning the "air law" if you want to hour build there - so do a few hours dual training (which you would need anyway) and then do the flight test - get a full FAA license.