The first local elections requiring residents to show ID were ‘well run' but the new law prevented some eligible voters from casting their vote, according to the Electoral Commission.
Commenting on yesterday's polls, a spokesperson for the commission praised the hard work of electoral administrators in preparing for the implementation of the voter ID law.
However, it cautioned that ‘confidence in the overall picture' should not overlook the impact of the requirement to show ID at polling stations.
A spokesperson said: ‘We already know from our research that the ID requirement posed a greater challenge for some groups in society and that some people were regrettably unable to vote today as a result.
‘It will be essential to understand the extent of this impact, and the reasons behind it, before a final view can be taken on how the policy has worked in practice and what can be learnt for future elections.'
The Association of Electoral Administrators said polling day had ‘run as smoothly as usual, without any major issues'.
AEA chief executive Peter Stanyon noted there were ‘anecdotal reports' of people being turned away because of a lack of ID but said it was ‘still too early to gauge how introducing voter ID has gone'.
Chairman of the Local Government Association's people and places board, Kevin Bentley, said: 'It is vitally important that the Government works with councils, the Electoral Commission and all those involved in elections to rigorously and transparently evaluate the implementation of voter ID at today's elections to ensure lessons are learned ahead of future elections.'
