Some local authorities have sent polling cards and postal votes to a ‘small number' of non-eligible European Union (EU) citizens following a glitch with elections software.
The Electoral Commission said it had resolved the problem and the names will not appear on electoral registers used at polling stations.
It has written to Brexit campaigners Iain Duncan Smith and Bernard Jenkin to explain the situation after they voiced ‘serious concerns' about the conduct of the referendum.
An Electoral Commission spokesman said: ‘We are aware that a small number of non-eligible EU citizens had mistakenly received poll cards and, in some instances, postal votes for the EU referendum.
‘We are working to confirm the exact number of electors who have been affected by an issue with elections software.
‘The software provider has resolved the issue which means that, if any postal votes have been issued to these electors, they will be cancelled and none of these electors will be shown as eligible on the electoral registers to be used at polling stations on 23 June.'
The spokesman added that local electoral registration officers would be writing to affected people to inform them they are not eligible to vote in the referendum after all.
Issues came to light after a Polish man in the London borough of Kingston-upon-Thames received a poll card for the referendum because he had stated he was British on his application for registration.