Tasmanian women will be able to access surgical abortions, with a private provider to begin offering the procedure later in the year.

It follows outrage over the sacking of Cricket Australia staffer Angela Williamson after she criticised the Liberal state government for a void of abortion services.

Tasmania’s only dedicated surgical clinic closed in Hobart late last year but a new low-cost private provider would open by October, the health minister, Michael Ferguson, announced on Sunday.

Advocates for greater abortion access said the announcement was better than nothing but still nowhere near good enough.

The news came as about 200 people rallied in Hobart in support of Williamson, who is taking Cricket Australia to the Fair Work Commission for unfair dismissal.

“We’re demanding access through the public health system and private, it needs to be both,” organiser Holly Ewin said.

She said she was “shocked and horrified” by Williamson’s sacking. “I couldn’t believe that somebody could be fired for having an opinion.

“I’m just angry and so are lots of other people and we’re not going away until we get what we’re demanding.”

The government said a patient transport and travel assistance scheme would be available for women needing to travel from other parts of Tasmania to access a surgical abortion.

The Hodgman Liberal government previously ruled out funding for the procedure through the public health system, instead offering assistance for women needed to travel to the mainland.

The Labor MLC Jo Siejka spoke at Sunday’s rally and said the new private clinic was too far away.

“It’s something that’s a legal right ... something that should be safe here and affordable to do here and not something that [Williamson] should have to go interstate at considerable expense to herself to get,” she said.

Williamson criticised on Twitter the government’s lack of abortion services after going to Victoria to have one.

Cricket Australia cited her “offensive comments” and “disparaging tone” in sacking the 39-year-old late last month, and the premier, Will Hodgman, later revealed the woman’s employer apologised to the government for her conduct.

Williamson’s legal proceedings before the Fair Work Commission are expected to begin later in August.