The senior Conservative MP said mass immigration had put unprecedented strain on education, health and jobs.
The former shadow home secretary also warned that migration was putting too much pressure on certain communities.
In an interview with BBC Look North, David Davis, said: "We are a tolerant nation. We accept people with open arms, but this challenges that.
"From the point of view of maintaining a civilised society, we need to change the rules and that has to be one of the conditions of us staying in the EU."
In a recent speech on immigration, Prime Minister David Cameron pledged to curb welfare for EU migrants coming to the UK - a proposal which would see workers from overseas prevented from claiming certain benefits for up to four years.
However, the Mr Cameron has so far ruled out a limit, or so-called "emergency brake" on EU migration - a move many Conservative backbenchers support.
Any proposal to cap the number of European migrants coming to the UK would be opposed by those who argue that freedom of movement is a fundamental EU principle.
Labour MEP for Yorkshire and the Humber, Richard Corbett, said: "There are almost as many Brits living in other European countries as there are EU migrants in Britain.
"Those EU migrants in Britain pay far more in taxes than they take out in benefits."
The recent debate around immigration has focussed largely on the arrival of citizens from Romania and Bulgaria into the UK.
Many argue that newspaper predictions about being Britain being 'swamped' by a new wave of migrants from Eastern Europe proved wide of the mark.
My colleague Sarah Corker travelled to Romania to produce a special report for Sunday Politics in Yorkshire and Lincolnshire.
She found that many Romanians are worried about young, skilled workers leaving the country, creating a 'brain drain' in hospitals, schools and universities.
Former Europe minister David Davis has called for a cap on the number of EU migrants coming to the UK.