Article 18 of the UK / Cyprus double taxation agreement, which can be found at:-
Cyprus-UK Double Taxation Convention as amended by the 2018 Protocol – in force
advises that salaries, wages and other similar remunerations paid by the UK government, is respect of work rendered to the UK,
shall only be taxable in the UK, unless you are a national of Cyprus.
Any non government employment, even on the base, will be taxable in Cyprus.