Flights could be a problem. There are two airports in southern Cyprus, Paphos (39 miles from Limassol) and Larnaca (44 miles from Limassol). Scyscanner.net shows that there are, at some times, flights to both these airports from Birmingham, Bristol, Cardiff, East Midlands, Glasgow, Gatwick, Luton, Manchester, Newcastle & Stansted (to Paphos only). I've tried every combination of departure and arrival airports for the dates you require and the only suitable flights on offer are from Gatwick to Paphos with First Choice. The outbound flight leaves at 0730, arriving at 1410. The return flight leaves at 2105, arriving at 0005. Total flight costs, including taxes, are �186.91 per person.
http://www.skyscanner.net/
(Stop Press: Its only �179.50 if you book direct with First Choice! :
http://www.firstchoice.co.uk/flights/ )
(More Stop Press: I've just found that Cyprus Airways are offering return flights from Heathrow to Larnaca on the dates you require but, since they're charging �254 before taxes, I'll assume that you'd prefer the Gatwick flights. See here for more information:
http://www.cyprusairways.com/ )