Union leaders in Glasgow have been told they face legal action for allegedly organising illegal pickets and wildcat action as a strike by 8,000 mostly female cleaners and care workers over equal pay enters its second day.

Lawyers for Glasgow city council wrote to the GMB union to accuse its officials of organising an illegal walkout by 600 street cleaners and refuse workers, and of setting up pickets that intimidated people not involved in the dispute.

The industrial action spread further on Wednesday morning, when more than 50 parking attendants refused to cross picket lines and were sent home.

GMB officials denied there were any unlawful pickets or orchestrated wildcat strikes.

“We will not be bullied by any employer, much less Glasgow city council,” said Rhea Wolfson, a GMB organiser. “It is shameful an employer like Glasgow has threatened to use Tory anti-trade union legislation against working-class women, and working-class men who have huge sympathy for these women.”

On Tuesday street sweepers, road workers and refuse workers, nearly all of them men, refused to cross picket lines.

The strike, which has led to primary schools and nurseries across the city being shut for the second day running, is thought to be the largest ever in the UK in a dispute over equal pay. The claims, estimated by union advisers to be worth up to £1bn, affect 12,000 staff and stretch back more than a decade.

After the refuse collectors and street sweepers refused to work, the council threatened to invoke trade union legislation introduced by the Conservative government in 1992 unless the GMB formally repudiated their unofficial action.

Carole Forrest, the council’s solicitor, wrote: “If no repudiation is forthcoming, we reserve the right to raise proceedings against the GMB for the losses which we have sustained as a result of this unlawful action and any repetition of it tomorrow.”

Council sources said the GMB was also asked to stop pickets being set up at council depots and offices which, the council said, were attended by non-strikers. One source said that in some cases cars were being hit by placards, intimidating drivers.

The council said the letter, leaked to the Sun, was a warning to reinforce its formal position about the unofficial strikes, but that it had no plans to take the GMB to court.

“We are not going to take them to court but we cannot just accept that wildcat strikes are part of the landscape. It is unacceptable to just shut the city down without giving us a chance to plan for it and to mitigate the damage, or address the concerns of workers who are withdrawing their labour,” one senior source said.

Wolfson denied the walkout by street sweepers, bin collectors and road workers was orchestrated by the GMB, or that the pickets were unlawful. “Individuals have exercised their consciences in choosing to support the action. It hasn’t been encouraged by the GMB,” she said.