As has been said, with an EASA CofA machine maintained to the CAA Light Aircraft Maintenance Programme (LAMP) there is a permitted variation for the Annual of 1 month - one handy thing to come out of EASA.... See Section 4, Page 1, Para 2.
There are some provisos though such as it does require an 'inspection' to issue the variation (as with any variation/extension).
If it still can't be done this way then you need an EASA 'Temporary Permit to Fly' (application form SRG 1733 from the CAA website). This form is 'applicable to UK registered EASA aircraft types for which a Permit to Fly is required due to the Certificate of
Airworthiness being temporarily invalid'.
I have a feeling that the Annual inspection must be carried out at an approved organisation's facility, but I stand to be corrected.