The Fine Gael leader issued the warning as he met with Irish people living in London yesterday in a bid to convince them to register to vote before the June 23 decision.
Speaking as he attended the Mayo v London All-Ireland GAA match, Mr Kenny said a “substantial” percentage of the British electorate are Irish citizens who could ultimately decide the referendum result.
The Taoiseach, who is taking part in an Irish Government attempt to convince citizens in Britain to vote in the referendum, said “our wish is Britain would stay as a strong member, a central member, for the time to come”.
He added that, if Ireland’s nearest neighbour leaves the common market, this country will be among the first to suffer.
Mr Kenny, Foreign Affairs Minister Charlie Flanagan, minister of state Paul Kehoe, and Communications Minister Denis Naughten are all due to visit Britain in the coming days to emphasise the need for a vote to remain in the EU.
About 500,000 Irish citizens live in the UK.