The Home Secretary was inspecting cross-Channel border controls, and security at Calais and the Channel Tunnel, with the French interior minister Claude Guéant today.
Mrs May said she was concerned about people from North African countries caught up in the Arab Spring unrest trying to settle in Britain.
Although the exodus had not yet reached Britain, she said: “We need to look ahead at what might happen in the future.” European countries should look to stem the migrant flow at its source, she said.
She added: “We very much feel that we should be working with countries in North Africa, like Tunisia, to provide practical support through the EU for them to be able to exercise controls on their borders.”
Mrs May said Britain wanted to co-operate practically with France to ensure that North Africans did not try to come to Britain.
Joint operations between UK and French officials have already helped cut the number of people trying to get to Britain from the Port of Calais by 70 per cent, she said.
Mrs May said “strong practical action was needed”, adding: “We need lasting practical co-operation and not burden-sharing.”
Under the Schengen Agreement, citizens in 25 mainland European Union (EU) nations are allowed to travel across borders without having their passports checked.
Tensions have risen over the fleeing migrants after Italy handed more than 25,000 Tunisians temporary permits to travel, effectively giving them unobstructed travel around the 25 EU nations. The UK and Ireland are not part of the agreement.
Mrs May also said she was focused on ensuring that illegal immigrants did not try to use the 2012 Olympics as a reason to get into the UK.
She said: “We have a joint cause in trying to ensure we stop illegal immigration and in making sure access to the Olympics is secure.”
The Home Secretary also defended the work of the UK Border Agency (UKBA), which was described as “not fit for purpose” by MPs last week. They accused the agency of running an “amnesty” for asylum seekers in an attempt to clear a historic backlog of 450,000 cases.
But Mrs May said the UKBA was “doing an extremely good job” and added that the coalition Government had inherited the backlog from Labour.
Shadow Home Office minister Gerry Sutcliffe said the immigration system was “in disarray”.
He said: “Practical international cooperation is undoubtedly crucial for the effective policing of our borders but it will take more than a visit to Calais to get the fair enforcement of immigration controls right.”
Mrs May is expected to unveil plans for a new National Crime Agency, bringing together officers from the Serious Organised Crime Agency, the police and UKBA in the next few days.
Prime Minister David Cameron has pledged to reduce net migration to the tens of thousands by 2015 but figures released last week showed it hit 242,000 at the end of last year–its highest level in more than five years.