Speaking after addressing the EU parliament in Strasbourg, Mr Kenny also said he couldn't see any renegotiations of European treaties, as suggested by some in Britain.
Mr Kenny hinted that any such moves could lead to more referendums in Ireland.
"I think it would be catastrophic if Britain were to leave the European Union," the Taoiseach said.
"I regard myself as a close working, political friend of Prime Minister Cameron's. We signed a strategic partnership agreement with Britain last year. We have very close relationships obviously, with our closest neighbour, both in trade and economics and all the rest of it."