I think they are pushing you in the wrong direction, the requirements for ATPL can be found on the UK CAA website. It clearly states that an ICAO licence is valid and there is no need for you to change your licence. I hold a South African PPL and am currently completing my Jar ATPL as well as many other pilots
Who ever gave you that info must read up
follow this CAA LINK
http://www.caa.co.uk/docs/175/SECTION%20D.pdf with regards to the requirements.