Ms Cufley left her role despite surviving a no-confidence vote at a meeting of the Shepway Liberal Democrat group, which is fighting government plans to cap its council tax.
Continuing political turmoil has also led the council to postpone the appointment of a new chief executive.
Interim chief executive Brian McAndrew said: 'I am now making the necessary arrangements for the council to elect a new leader and for him or her to choose a new cabinet.'
An arm's-length management organisation will be set up in Nottingham following council tenant approval.
Tenants voted 76% in favour of the ALMO which will consist of councillors, tenants' representatives and independent professionals.
Nearly 15,000 council tenants and leaseholders took part in the ballot, a turnout of 40%.
Nottingham is now eligible for up to£165m from the government to modernise its council houses and flats.
The organisation will employ existing housing department staff under direction of the board.
Council houses will still be owned by the city council, which will continue as landlord.
UK Sport has developed a forecasting model that can be used to calculate the potential economic benefits of hosting large sports events.
It said the bulk of extra spending came from spectators, on average just under£50 per day, while members of the media spent£100 daily.
The quango's major events director John Scott said: 'Economic impact is understandably one of the key factors taken into account by councils when assessing whether or not to bid for an event, and this research strongly demonstrates the significant financial benefits that result.
'The model will be crucial in allowing accurate assessments on which to base decisions.'
Melton BC chief executive Delwyn Burbidge is leaving after three years to become chief executive at Maldon DC.
He will replace Steve Packham, who became chief executive of neighbouring Chelmsford BC following the retirement of Martin Easteal.
Melton leader Malise Graham (Con) said Mr Burbidge had arrived when the council was at low ebb and 'his greatest legacy to us is that, after a period of instability, confidence has returned'.