What does Central and Eastern Europe make of the prospect of the UK leaving the EU? The chances of a British exit, or Brexit, have certainly risen. During the third week of February, Prime Minister David Cameron, who has long backed the UK staying in, confirmed the referendum date of June 23. Almost immediately, the “Leave” camp began campaigning, aided by new recruit Boris Johnson, the colourful mayor of London.

The UK’s ruling Conservative Party is now deeply split over Europe, with the prime minister on one side and Johnson – by far the country’s most popular politician – on the other. With much of the media dismissing Cameron’s recent “renegotiation” with the EU as largely cosmetic, or worse, the Brexit drums are now banging.

Having shown “Remain” ahead for months, opinion polls now suggest the two sides are neck-and-neck, with some putting “Leave” marginally in front. As winter turns to spring, and evermore migrants cross the Mediterranean into the EU, many predict that public support for Brexit will rise.

It’s over four decades since the British public last had a say on Europe. Back in 1975, the UK voted decisively – two-to-one-in favour – to remain in what was then the European Community, known as “the Common Market”. Since then, European treaties such as Maastricht and Lisbon have considerably enhanced the power of what became the EU, at the expense of national sovereignty.

In addition, of course, the nine nation states of the mid-1970s EC have expanded into 28 EU members. These include eight former “Eastern bloc” countries that joined in 2004 – in a “big bang” enlargement symbolizing the unification of East and West Europe – followed by Bulgaria and Romania in 2007, and Croatia in 2013.

Central and Eastern Europe has recently featured heavily in the British press, in relation to Brexit. That’s because the Visegrad countries – Poland, Czech Republic, Hungary and Slovakia – initially looked like they could block the deal that Cameron so desperately needed. Britain has lately seen net migration of over 300,000 annually – in stark contrast to the prime minister’s “no ifs, no buts” pledge to reduce the figure below 100,000 back in 2010. Much of this influx has come from CEE.

As such, many British voters are now openly scornful of the EU’s “open border policy” – allowing workers to freely move between member states – which has galvanised support for Leave. So Cameron’s renegotiation needed to include measures designed to “discourage” migration from relatively low-wage CEE members.

The UK’s proposed “benefits brake” is designed to limit the extent to which EU migrants entering Britain can claim in-work benefits. This was vigorously opposed by the Visegrad Group, given the extent to which their citizens have gone to live and work in Britain, and will continue to do so. There are at least 750,000 migrants from Poland alone living in the UK. No wonder Cameron’s measures were seen as “blatant discrimination” by Polish Europe Minister Konrad Szymanski.

Despite spending considerable time travelling between CEE capitals in search of a deal, the British Prime Minister was repeatedly rebuffed. “Eastern threat to EU deal”, screamed one UK newspaper. “Cameron is Eastern blocked”, declared another.

The agreed compromise, shaped by the Visegrad Group, means EU migrants receive in-work benefits phased in over their first four years in the UK, rather than the five-year outright ban Cameron wanted. Furthermore, these limits won’t apply to migrants already in Britain, but only new arrivals. Their introduction also depends on the UK convincing Brussels that heavy immigration is unduly pressuring public services. And, if introduced, this significantly weakened emergency brake will only apply for seven years.

While the Visegrad governments had to put up a fight to appease their own electorates, it is hardly surprising they did a deal with Britain. Such countries view London as a natural ally within the EU – and would be loath to see Britain leave. Broadly sceptical of Europe, fiercely protective of domestic sovereignty and keen to cut red-tape, the Visegrad Group need a major Western European EU member that sees the world their way. Such countries view Britain as vital, in particular, as a counterweight against the influence of the all-powerful Franco-German axis.

The role of Russia in the UK’s Brexit debate will grow as we approach the referendum. Already, with determined repetition, the Remain camp consistently claims “Russian aggression” and “Putin’s desire for Brexit” are good reasons not to leave.

Already this crude tactic is backfiring, with many senior British military leaders pointing out the UK’s security rests not with the EU but Nato, an organisation Brussels has often tried to undermine. But that won’t stop Russia being increasingly used as a campaigning tool by the British government and other Remain supporters ahead of the vote in June.

Liam Halligan is Editor-at-Large of Business New Europe. Follow him on Twitter @liamhalligan