MADRID/DUBLIN (BLOOMBERG) - The future of bankers in Brexit Britain may be decided in the classroom, not just the boardroom.

With Prime Minister Theresa May planning to trigger the start of negotiations to leave the European Union by the end of March and now pledging also to quit the single market, the continental contest among cities to attract finance jobs has been heating up. The focus so far was on office space, guaranteed access to European markets and potentially lower living costs for bankers.

But a new life outside the UK may also mean a change of school for their children, and there's already an increase in requests about available places in Paris, Dublin and Madrid, senior staff at international schools said.

"In a period of three weeks, I must have had inquiries from some 20 families of people in the financial industry in London, which is totally atypical," said Frank Powell, headmaster of Runnymede College, a British school to the north of Madrid with about 850 pupils. "Practically all of them prefaced this by saying they may be moving to Madrid." Where Next?

Bankers are still assessing what Brexit may bring. A report by Oliver Wyman on behalf of TheCityUK lobby group in October estimated that almost 70,000 jobs are at risk from a Brexit deal that withdraws Britain from the single European market. Banks want to retain "passporting" rights, which allow them to do business across the EU.

At HSBC Holdings, one of the most globalized banks, chief executive officer Stuart Gulliver said this week that trading operations generating a fifth of revenue for the lender's investment bank in London may move to Paris.

"Activities specifically covered by EU legislation will move," he told Bloomberg Television at the World Economic Forum in Davos.

An alluring lifestyle may be the clincher when it comes to siphoning jobs out of London. And with pressure on places, schooling is one area that might make the difference.

"A major consideration for individuals will be around schooling and their families, and London is very difficult to beat in that regard," said Jamie Risso-Gill, a director at executive search firm Per Ardua Associates in the UK capital. "London for many years has been set up and geared up for that. I can't think of a rival city that can offer anything like a similar setup."

Families moving out of London should make their arrangements for their schooling well in advance, particularly is cities such as Geneva where capacity is already stretched, said Susan Krumrei, head of field research and consultant for Europe for the UK-based International Schools Consultancy. At Runnymede College in Madrid, for example, there are 40 vacancies a year filled to capacity for the last decade, Powell said.

"Some admissions departments, particularly in leading European cities including Frankfurt and Geneva are already receiving an increase in the number of enquiries in preparation for a potential relocation from London as a result of Brexit," said Krumrei. "The leading international schools in all of these cities are close to capacity and some have waiting lists for certain school years."

Paris aims to lure as many as 20,000 workers from Britain's finance industry, according to Europlace, the French capital's lobby group. In Spain, the market regulator is setting up a fast-track authorization service in English.

Ireland is another possible destination for companies based in Britain, not least because of the proximity and shared language. Ireland's minister in charge of financial services said in an interview this week that the prospect of losing access to the EU's single market should lead to a wave of UK-based companies to announce they are relocating jobs to Ireland by the middle of this year.

When it comes to education, the Irish government has said it's considering setting up a school that offers an international education based on the baccalaureate. At St Kilian's German School/Eurocampus in Dublin, the phone has been ringing more from overseas parents.

"How many of those are specifically because of Brexit is hard to say," said Alice Lynch, principal of the school, which has 722 students from kindergarten through secondary school. "At the moment, it seems parents are trying to get the lay of the land rather than making firm decisions on school places."

Applications are also up for places at Marymount School, an international school in Neuilly near Paris that teaches 360 children from nursery to eighth grade, said Kate des Places, external relations director. "People tend to be very discreet about their reasons for moving," she said.

TIC Recruitment, a careers website for international teaching posts, canvassed school heads for their views on Brexit. Peter Kotrc, director of the Brandenburg International School in Berlin, told TIC that cities like Frankfurt that will likely attract banks away from the U.K. "will experience further pressure on school places and new schools will open."