Commenting on allegations made on Channel 4 News, Liberal Democrat Brexit Spokesperson Tom Brake, said:
"These allegations are stunning and touch directly on one of Theresa May's closest advisors.
"The British people expect fair play and campaigns to abide by the rules – they must not be cheated. These allegations must be examined by the police. If they represent what happened it is outrageous and shameful.
"The referendum had a very narrow outcome. One of the biggest exercises in democracy must not turn out to be one of Britain's biggest electoral frauds."