Williams crashed into a tree last Thursday (June 23), admitting she had made an "error of judgement" by getting behind the wheel following "several glasses of wine" - and to make matters worse the incident occurred shortly after Williams had spoken to families of people killed in drink-driving incidents.

No charges have been filed but police are investigating.

Williams stepped down from the Brisbane 2032 Board of Directors as a consequence, but has so far resisted calls to also resign as Mayor of Redland City Council.

Two petitions have now been launched demanding Williams' resignation.

Judy Lindsay, whose daughter died in a crash involving a drink-driver and was a part of the meeting with Williams on June 23, started a campaign on the Queensland Parliament website.

It so far has a little more than 3,180 signatures.

A duel campaign on the change.org platform, set up by Rick Young, has more than 4,600 signatories.

Williams was among the Organising Committee Board's initial 21 members, with the group formally completed in April.

She was nominated by Adrian Schrinner, Brisbane's Lord Mayor. 

Redland City is within the Brisbane metropolitan area.

Three officials have already left the Brisbane 2032 Board.

Ex-Sports Minister Richard Colbeck and Ted O’Brien, who was Special Envoy for the Brisbane 2032 Olympics and Paralympics, were both removed following May's general election, when incumbent Scott Morrison lost and Labor's Anthony Albanese became Australia's new Prime Minister.