CAIRO, May 2 (Reuters) - Britain welcomes a deal brokered by Egypt to end a four-year feud between Palestinian factions Hamas and Fateh, Foreign Secretary William Hague said on Monday.

Israel has condemned last week's surprise unity deal between Islamist group Hamas, which administers the Gaza Strip, and Fateh, which exercises limited self-rule in the West Bank, saying it will sabotage prospects for peace.

Fateh says unity among Palestinians is vital for any progress towards statehood.

We welcome the reconciliation (of Hamas and Fatah) and the work done by Egypt, Hague told reporters in Cairo after meeting Egyptian Foreign Minister Nabil Elaraby.

Of course lots of details have to be worked out and we will have to judge everyone by their actions and intentions. We will continue to work closely on this, he said.

British Prime Minister David Cameron was the first foreign leader to visit Egypt in February after President Hosni Mubarak was overthrown in a popular revolt.

Hague met the head of Egypt's ruling military council, Field Marshal Mohamed Hussein Tantawi, and interim Prime Minister Essam Sharaf.

He said NATO would intensify military operations in Egypt's neighbour Libya, where leader Muammar Gaddafi is fighting an insurgency against his four-decade rule.

Time is not on the side of the Gaddafi regime, said Hague. The policy is to continue to increase pressure on the Gaddafi regime -- diplomatic, economic and military pressure. We have increased the pace of the military operations under UN resolution 1973 and will go on doing so.

(Reporting by Tom Pfeiffer; editing by Andrew Roche)