Technically , you are correct - under the DPA you are entitled to see a copy of the letter (you may have to pay a fee - up to £10 , I believe - usually waived). If the Elders have refused point blank saying that you are not allowed then they are wrong. There is no excuse for this - the elders have received numerous letters on the DPA and the WTS has bent over backwards to comply.
HOWEVER:
(1) The letter is destroyed as soon as it is read , so it may no longer exist. The original congregation does not keep a copy.This overcomes any problem with data storage and processing under the act.
(2) In the highly unlikely event that your new congregation has kept a record , the letter is unlikely to be of any value anyway. The elders are told to keep any written information as vague as possible , so it is unlikely to be prejudicial. The last letter we received simply stated the persons name , very brief outline information and how long they had been in their previous cong. The new PO will normally phone the old PO (or vice versa) and any meaningful information is passed on verbally.
Information about data protection is contained in this link: http://www.opsi.gov.uk/acts/acts1998/19980029.htm