Bromley, Gosport, Swindon, Watford and Woking are all testing the scheme, which aims to cut down on voter fraud.
MPs and councillors have spoken on social media of incidences of people, including elderly residents, being turned away from polling stations for not having the right ID.
Angela Wilkins, leader of Bromley’s Labour group, said she knew of five people being unable to cast a ballot because of the pilot and that the scheme caused long delays in the south London borough.
She wrote on Twitter: “Just been round the C Palace polling stations. 5 people not able to vote due to #voterID pilot and several walked away because of queues @CatSmithMP @labour4bromley. So why are we doing this .@LBBromley ?”
The presiding officer at one Bromley polling station said “only a very small percentage” of voters had forgotten or were unable to present identification.
The man, who did not want to be named, said people in the borough had been sent five pieces of information alerting them to the impending changes, including leaflets and a note with their polling cards.
He added: “Voters always have the choice to go home and get some ID.”
Labour’s Ellie Reeves, MP for Lewisham West, said two people were turned away from voting on Thursday morning because they did not have ID.
She tweeted: “Just been to vote. Was informed that two people had already turned up without ID this morning so had been unable to vote. Very worrying and backs up all the evidence that the voter ID pilot in Bromley is plain wrong.”
One elderly resident who was turned away for not having a bank card or passport told the Independent he was “shocked” to be denied the right to vote, describing the ID scheme as “nonsense”.
Meanwhile, Bradford Council has apologised after a presiding officer turned away voters for not bringing photo ID, despite none being required.
A spokesman said a “very small” number of voters were affected at one polling station in Shipley, adding: “We were alerted to the matter early this morning and it was dealt with immediately.”
Cat Smith MP, shadow minister for voter engagement, said the Government had been warned the trials would have a “disproportionate impact on older people, young people, BME communities, trans people and disabled people”.
She described the scheme as being akin to using a “sledgehammer to crack a nut”.
“The Electoral Commission found that out of nearly 45 million votes cast in the local and General Election in 2017, there were only 28 cases of alleged voter fraud. That’s less than 0.00007% or one case for every 1.6 million votes cast. And out of those 28 cases, there was only one conviction.
“But instead of listening to the experts and the vast evidence base, the Government decided to implement a mistaken policy with the full knowledge that voters could be disenfranchised.”
The Electoral Reform Society warned last week that the plans were “deeply flawed” and amounted to a “calculated effort” to “make voting harder for some citizens”.
The Government said before polling day that it was trialling the new rules to “improve the security and the resilience of the electoral system that underpins our democracy”.
Ministers said it was “proportionate” to ask people to prove who they are before they vote, when that is already incumbent on people to claim benefits, rent a car or collect a parcel from the Post Office.
An Electoral Commission spokeswoman said: “Returning Officers administering the elections in the pilot areas have run awareness campaigns to inform voters of what form of identification they need to bring in order to be able to vote.
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“We encourage anyone who has queries about the pilots to contact their local council’s electoral services department.”
:: Sky News will bring you live coverage of the local election results on web, mobile and TV on Thursday night and throughout Friday. A live blog will be running throughout the night, while a special programme will provide analysis of the results as they come in hour-by-hour.