"The EU deals with so many different subjects that there is no permanent bloc of member states within it," Maasikas told BNS. "Discussion among member states is always going on over different subjects in like-minded groups."

The Financial Times said on Tuesday that European diplomacy has long been built around alliances, and few have a more glorious history than the Hanseatic League — a 14th century grouping of Northern European trading powers that helped drag the continent out of the Dark Ages. On Monday night, finance ministers from the Baltic states, Nordic countries, and Ireland had dinner together in the Belgian capital, and the Dutch and German ministers also swung by for coffee. It's an uncanny echo of the old League, which stretched around the Baltic, the paper said, adding that this marked the second time a version of the club had met in the past few weeks.

"We hold very much the same opinions with these countries, but not always," Maasikas said. "But it's clear that Brexit has given rise to certain new dynamics in the European Union."

The Estonian official highlighted that the exit of the U.K. from the union will significantly weaken the group of countries not using the euro. "Where so far, the U.K. saw to it that the interests of the countries not using the euro were not forgotten when it came to monetary policy matters in the eurozone — such as in matters related to the banking union — this group would now be much smaller. Following Brexit, the eurozone will account for 80-85 percent of the EU's GDP. "Here we will definitely have a shift in dynamics," he added.

"The U.K. has been standing up very firmly for strengthening free trade and the internal market," Maasikas continued. "In this, member states are also looking for how to move forward. It is absolutely clear and a known fact that Estonia and the Nordic countries have been and remain very strong proponents of free trade nd there has been coordination among the like-minded group."

Likewise, changes have taken place on the subject of the EU budget, the Estonian official said, where there exists a group of net payers and a group of friends of the cohesion policy, i.e. net beneficiaries. "Depending on the topic such meetings and coordination are going on all the time," he added.

Member states favoring closer EU integration also often look toward each other, according to Maasikas, and on that topic, Estonia has been working closer together with the other Baltic countries and the Nordic countries. "But the new situation, new dynamics make Estonia seek, of course — again, depending on the topic — cooperation with some geographically more distant but also pro-integration member states such as Spain, Portugal, Slovenia, and Cyprus," he said.

"Howver, there is a certain period of seeking out new constellations, new cooperation now," the official noted. "Since there has been talk of major changes within the EU, all member states are considering how their interests will be protected. Institutional EU issues — issues of division of power, that is — also remain, where polarization is more along the lines of big and small member states. But it isn't worth paying too much attention to one specific meeting."

The Financial Times cited an unnamed diplomat as saying the "club" was a direct response to Brexit, as well as further developing longstanding Nordic and Baltic cooperation. The coming together was a "natural" reaction to the U.K. departure, and to recent moves by Paris, in tandem with Germany, to drive the EU agenda, added the diplomat.

With the U.K. leaving, "small and medium-sized countries are realizing that they need to make their voices heard," another national official said according to the paper. While the countries are far from united on all EU policy issues, they share a common outlook on many economic questions, favoring dynamic competition on the single market, and stressing the need for national budgetary responsibility within the eurozone.