The authority had planned to vote on its committee chairs yesterday but the full council meeting was cancelled at late notice after Cllr Jane Mortimer quit the Conservative group.
The Fylingdales ward councillor confirmed to the Local Democracy Reporting Service that she would now be sitting as a member with no political affiliation following her decision to leave the group.
Cllr Mortimer said she had not quit the Conservative Party but would no longer be a member of the council’s opposition group.
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She said: “It’s been a very difficult decision to come to after 30 years but there are things going on that I did not agree with.”
“I will still be a member of the Conservative Party. I will still serve my community, go to meetings and lobby for them and do what I have done for the last 30 years and be part of my community and work with them.”
In response, Cllr Heather Phillips, deputy leader of the borough council’s Conservatives, thanked Cllr Mortimer for her service to the group.
She added: “Some people have adapted better than others to being a party of opposition. It is a lot more difficult to be in opposition, especially for the members who have been there for a very long time.
“Unfortunately, evolution has been a bit more painful for some rather than others. The ones who have not been there as long have adapted better.”
Cllr Mortimer’s resignation leaves the Conservatives with 13 of the council’s 46 seats, the same number as the ruling Labour group.
The share of seats on committees is worked out on a percentage of the total membership of each group.
Over Christmas and New Year three councillors left the Independent Group, which runs the council alongside Labour.
Guy Smith, Roxanne Murphy and Eileen Murphy have all since joined the Yorkshire Coast Independents Alliance (YCIA) alongside councillors Neil Heritage and Sam Cross, who have both previously represented UKIP on the authority.
Cllr John Atkinson, previously of no political affiliation, also joined Cluster of Independent Members at the end of last year.
The fallout of all these moves has left the council with a new make-up.
Labour and the Conservatives both have 13 seats, followed by the Independent Group with seven, the YCIA now has five, the Cluster of Independent Members has four and the Green Party two.
Cllr Mortimer is now listed as having no political affiliation along with Cllr Helen Mallory, who left the Conservative Group herself last year.
A date for a new meeting to decide on membership of committees has not yet been set.