The European Commission will release a report into the conduct of member states in organising this week’s European elections, following complaints from EU citizens living in Britain that they were denied votes due to administrative errors.

A spokesperson told reporters in Brussels that the Commission would look “very carefully at the conduct of elections” and look for lessons that could be drawn, adding that member states are required by EU law to “ensure that EU nationals can effectively exercise their voting rights”.

British nationals living abroad in the rest of the bloc and EU nationals living in the UK – both intimately affected by Brexit – complained on Thursday that they had been turned away from polling stations or had not been delivered their postal votes in time.

Both groups of people have the right to vote but there are widespread reports, both documented by campaigners and on social media, of people not being able to cast their ballots.

Cabinet Office officials in Whitehall blamed local returning officers for the problems, but campaigners also blasted the government for presiding over an out-of-date and bureaucratic system, and providing local authorities with limited resources.

The UK’s own Electoral Commission said it understood the “frustration” of citizens “finding they are unable to vote today when they wish to do so”, and blamed the government for not reforming electoral law to make the system more straightforward.

“The organisation of elections is the responsibility and competence of national authorities. As for the European elections the EU rules are directive 93/109 EC if you want to read that up and it requires members states to ensure that EU nationals can effectively exercise their voting rights,’ a spokesperson for the European Commission told reporters in Brussels on Friday.

“National authorities are in particular required to inform EU national voters residing in their territory in good time and in an appropriate manner of the conditions and details arrangements of the exercise of their right to vote.

“As it did in previous European elections the Commission will produce a report assessing very carefully the conduct of elections in all member states and also the lessons drawn that we can then learn from this.”

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EU leaders are expected to be presented with a draft of the report at a summit in Brussels at the end of June, which Theresa May is expected to attend. The final report will be delivered in the autumn.

While the UK and the Netherlands cast their votes on Thursday, other EU member states will not have finished voting until 10pm on Sunday evening, when the final results will be announced across the continent.