The Society of Dorset Men has admitted its first female member in 120 years, becoming the latest in a line of Victorian-style men-only clubs to allow women to join.

Elizabeth Day has been approved by the society, which was founded in 1904 to encourage men from Dorset to socialise in London, after the committee voted to allow female members in August.

After pressure from campaigners, the influential Garrick Club – founded in 1831 and boasting as members dozens of lords, ministers and civil servants, high-profile actors, senior lawyers, artists and even King Charles III – caved to criticisms of gender discrimination and allowed women to join this year. Mayfair’s Flyfishers’ Club, founded in 1884, voted to allow women in October after accusations of elitism.

Peter Lush, the chair of the Dorset society’s committee, told the Guardian: “This is little Dorset down on the south coast, not the Garrick Club at all.” He said women had always been included in the society’s functions and events, as well as annual general meetings. “It felt time and right to go the next step, and allow them to become members and allow them a vote and a say in our doings.”

During a special general meeting in August, a vote was held on admitting women – which required a two-thirds majority of those present – with 28 votes for and 12 against.

“There has been a certain amount of pressure for this change for some while,” Lush said. “Reaction [from wider members] has been quite slight, which tends to suggest the majority had no real issue with it either way.”

The Society of Dorset Men’s objectives include promoting “good fellowship among Dorset men wherever they may reside”, fostering “a love of the county and pride in its history and traditions”, and assisting Dorset companies and individuals “in need of the influence and help of the society”.

The name will remain unaltered, however, after a separate motion to retitle it the “Society of Dorset” was rejected.

Lush, 85, from Dorchester, said the society’s traditions “haven’t come to a shuddering halt. They’ve been given a boost, to make sure they continue into the future.”

Day, the first woman among about 720 male members, who pay £15 a year, said she felt “privileged and excited to be the first female member of this wonderful society”. Her husband, Bob, is also a member.

During the 19th century, membership of a “gentlemen’s club” was seen as a key way to have influence within public life. St James’s, in London, was packed with men-only societies, many of which survive today.

While there have been attempts to break the gender exclusivity over the years, a reckoning was sparked this year when the Guardian revealed the membership of the Garrick Club, exposing its grip on key flagpoles of the British establishment.

Several London clubs still refuse women, including the Savile Club, Boodle’s, the East India Club and White’s. Some are understood to have consulted lawyers after the Garrick vote – which rested on legal advice that the pronoun “he” in the club’s rulebook should also be taken to mean “she”.