In response to a Freedom of Information request, Thames Valley Police have admitted that no fingerprints were found on that mobile phone.
For completeness, I reproduce the information in the form received from Thames Valley Police here (I've put my questions in italics below):
Dear Dr Watt
Reference No: RFI2010000840
Thank you for your request for information dated 05/12/2010 which I have repeated below with our response to each point.
Was the mobile phone found in the Barbour jacket pocket of David Kelly on 18th July 2003 tested for fingerprints?
Were any fingerprints found on the mobile phone?
If the answer to 2 is "Yes", whose fingerprints were found?
Please contact me quoting the above reference number if you would like to discuss this matter further.