I have a UK visa that I have already used a few times to get into the UK. Can I enter Cyprus using this visa?
No. If you are a visa national, a UK visa does not allow you to enter Cyprus. Holders of the following documents do not need a visa, as of 17 June 2014, to travel to Cyprus:
Schengen Visa rated for two or multiple entries.
Schengen Long Stay Visa.
Residence permit issued by a Schengen Country.
Romanian, Croatian and Bulgarian Visa, Valid for two or multiple entries.
Residence permit issued by Romania, Bulgaria and Croatia.