Britain's Union Jack national flag is pictured during a debate on Britains withdrawal from the EU during a plenary session at the European Parliament on January 16, 2018 in Strasbourg. FREDERICK FLORIN | AFP | Getty Images

Britain's departure from the European Union (EU) could paralyse law-making in Brussels for at least 5 years. Brexit may now not happen before October 31st, after European leaders agreed last week to allow more time for Prime Minister Theresa May and the U.K.'s parliament to sort out the country's exit from the EU. But if current divergences in London over Brexit are not solved by May 22, then Britain will have to take part in European Parliamentary elections — opening unprecedented legal and political challenges to the EU. Holding EU elections in the U.K. is set to fatally affect the good functioning of the next European Parliament (the EU's legislative arm) – as well as the entire Union – for the five years to come, two European law experts told CNBC in emailed remarks. Not only the British participation in the elections is set to distort the new political balance emerging within the new Parliament, but also to irremediably tarnish the validity of the Parliament's future decisions, Alberto Alemanno, Professor of EU law at HEC Paris, and Benjamin Bodson, researcher in EU law at UCLouvain said. European citizens elect new lawmakers to the European Parliament every five years. Following the U.K.'s request to exit the union in 2017, the European chamber has prepared for the fact that 73 British members of the European Parliament would not be taking their seats.

It's not easy to explain to the French, to the Polish, to the Austrian citizens that again the country who is leaving the EU will have a major say in the future decision-making process of the EU. Manfred Weber Member of the European Parliament

The EU decided to allocate further seats to certain countries and keep some of the other seats empty for when new countries join the Union. This decision stated that the upcoming parliament would be formed by 705 members, from the 751 today; and it would award 27 extra-seats to 14 member states. However, with the possibility that the U.K. will remain a member until October 31st, the European Parliament is yet to agree what to do with the seat allocation. If it follows the old rules and 751 members of the European Parliament (MEPs) are elected, it will break the principle of "degressive proportionally" – meaning that countries such as Sweden, Austria and Spain will be less represented than other countries with similar population sizes, Alemanno pointed out, saying this would breach European law. But if the new rules remain and 14 European countries are allowed to get 27 out of the 73 U.K. seats, the question then becomes when these extra MEPs would be able to start their jobs.

"These soon-to-be MEPs could argue that the treaties ensure them a term of five years, not less, and require to start their position as soon as July 2, when the new European Parliament will be sitting for the first time (and not whenever the U.K. leaves)," Alemanno said. "On the other hand, 'temporarily' elected British MEPs could invoke the same provision to stay after the UK's withdrawal. This would lead the new European Parliament to have a record number of 778 MEPs," the law professor also said, pointing to another breach of European rules.

Political Difficulties

Legal implications aside, there are also political consequences of delaying the U.K.'s departure beyond the month of May. U.K. voters could have a strong say on who is the biggest political force at the European Parliament — ultimately influencing the direction of futures decisions. "It's not easy to explain to the French, to the Polish, to the Austrian citizens that again the country who is leaving the EU will have a major say in the future decision-making process of the EU. That is a political challenge ahead," Manfred Weber, the head of the conservative party at the European Parliament, told CNBC last week in an exclusive interview.