My friend has a lovely 1 bedroom apartment for rent in Limassol Cyprus. Only 250 euros per week. Suitable for singles or couples. About 40 mins drive from Troodos for skiing January to March, or 3 minutes walk to beach.
There are cheap flights available from Gatwick to Larnaca with Easyjet, though I don't think there are direct flights from Jersey, or only sometimes around October time, used to be through TravelMaker.
You can view the details here:
Comfy one bedroom apartment in Limassol for holiday rental