The mountain rating is an EASA qualification and the UK CAA should issue such a rating to the holder of a UK-issued EASA licence provided that the applicant has complied with FCL.815:
FCL.815 Mountain rating
(a) Privileges. The privileges of the holder of a mountain rating are to conduct flights with aeroplanes or TMG to and from surfaces designated as requiring such a rating by the appropriate authorities designated by the Member States.
....
(b) Training course. Applicants for a mountain rating shall have completed, within a period of 24 months, a course of theoretical knowledge instruction and flight training at an ATO. The content of the course shall be appropriate to the privileges sought.
(c) Skill test. After the completion of the training, the applicant shall pass a skill test with an FE qualified for this purpose. The skill test shall contain:
(1) a verbal examination of theoretical knowledge;
(2) 6 landings on at least 2 different surfaces designated as requiring a mountain rating other than the surface of departure.
(d) Validity. A mountain rating shall be valid for a period of 24 months.
(e) Revalidation. For revalidation of a mountain rating, the applicant shall:
(1) have completed at least 6 mountain landings in the past 24 months; or
(2) pass a proficiency check. The proficiency check shall comply with the requirements in (c).
(f) Renewal. If the rating has lapsed, the applicant shall comply with the requirement in (e)(2).
There are no 'surfaces' in the UK that are designated as requiring a mountain rating, nor do any UK based ATOs hold the necessary approval and so an ATO will have to be found elsewhere in Europe to conduct the approved course of training.