A bronze statue of Nancy Astor, the first woman MP to take up a seat in parliament, has been installed in Plymouth exactly a century after she was elected to represent the Devon city.

Theresa May unveiled the memorial, paid for through a crowdfunding campaign, on Plymouth Hoe outside Astor’s former home, watched by hundreds of schoolchildren and students.

May said Astor had to withstand the jeers and bawdy jokes of male colleagues – and the lack of female toilets – when she arrived in the Commons in 1919, but had paved the way for women MPs.

The former prime minister called for more women to play a part in public life and said she hoped there would be more statues of women. “We don’t have nearly enough monuments to the great women of our past,” she said. “I’m pleased we’re starting to put that right.”

Boris Johnson was in Devon on the campaign trail and went to view the statue after the unveiling ceremony – when the crowds had left.

Astor, a Conservative MP, was not the first woman to be elected. Sinn Féin’s Constance Markievicz won a seat in 1918 but, in line with the party’s abstentionist stance, did not take her seat in the Commons. The Astor statue has also angered many who criticise her as antisemitic, anti-Catholic and a Nazi sympathiser.

But focusing on Astor as a brave trailblazer, May said: “When Nancy Astor became the first woman to take her seat in the House of Commons 100 years ago our country and our democracy was changed for the better.

“Her arrival in parliament ushered in a new era, finally giving a voice to a huge swathe of the population who for too long had been missing from our politics and our lawmaking. It was the culmination of many generations of campaigning, protest, suffering and struggle.”

Astor, who stood down in 1945 and died in 1964 aged 84, also had a train named after her, the Nancy Astor Express, which travelled from London to Plymouth for the first time on Thursday. May said she hoped other women would travel from the south-west on it to take up seats in parliament.

Boris Johnson was campaigning in Devon and visited the statue with local Conservative candidate Rebecca Smith. Photograph: Stefan Rousseau/PA

Astor’s relationship with some male MPs was frosty and she is said to have told Winston Churchill: “If I were your wife I’d give you poison in your coffee,” to which Churchill supposedly replied: “If you were my wife, I’d drink it.”

On the frequently asked questions page of the statue campaign site, Astor scholar and keeper of the Astor archive Jacqui Turner addresses the question of whether the late MP was antisemitic, anti-Catholic and a Nazi sympathiser.

Turner, of Reading University, says: “The most controversial thing about Nancy Astor was the fact that she was a woman … Astor needs to be considered in the context of the period in which she lived, she made unpalatable statements in the heightened atmosphere of the years before world war two. Many male MPs escape such similar censure, Astor herself felt that it was because of her gender she was pilloried in this way.”

Lisa Berry-Waite, of Exeter University, who is researching the careers of the first women to stand for parliament, said: “Nancy Astor’s election success in the 1919 Plymouth Sutton byelection made headlines around the world and represented a new era for British politics. Parliament was no longer a male-only space and for the first time a woman was able to directly influence legislation.”