The cheapest way to phone the UK is on a local mobile, most phones brought over from the UK are locked here, if you can get an unlocked phone and use a local ''sim card'' it is remarkably cheap to phone internationally.
This will cost you £15 for a Cyta sim card that includes a number and some free calls, the number and calls last for over a year, so if you are regular visitors to CY this is the way to go, many buy a cheap mobile here for just this reason, £25 will buy you a low priced Nokia or another, Cyta (SoEasy) top up scratch cards start at £5 upwards but of cousre you usually have to have that sim card.
This could work out cheaper than using a UK locked or international roaming phone on the Island.