The awards celebrate excellence in the housing sector and the council has been shortlisted for its work on the regeneration projects for Biart Place and Rounds Gardens.
Councillors gave the green light to the regeneration plans after structural surveys commissioned by the council to gauge the future maintenance costs of the high-rise blocks revealed a number of issues caused by poor construction in the 1960s.
The council worked closely with experts from the Building Research Establishment to investigate options for repairing the five high-rise blocks at both sites but, when it became clear the blocks were beyond economic repair, work started on the regeneration plans.
Cllr Emma Crane, Rugby Borough Council portfolio for communities and homes, said: "The decision to move all the tenants out of Biart Place and Rounds Gardens, and find the tenants new homes while starting work on plans to regenerate both sites presented the council with one of the biggest challenges it has ever faced.
"However, from the start, the safety and welfare of our tenants has guided our decision-making and I'm proud of the way the council has risen to the challenge."
Working in collaboration with Warwickshire Fire and Rescue Service, the council changed the fire safety procedure at both sites from a 'stay put' policy to evacuation.
Personal Emergency Evacuation Plans (PEEPs) were drawn up for tenants requiring help to evacuate, while the council installed a new fire alarm system at Rounds Gardens to increase tenant safety.
Following the decant of Biart Place, firefighters from Warwickshire Fire and Rescue Services carried out a major training exercise at the high-rise blocks to test equipment and procedures - a rare opportunity to train at such buildings which has now informed the response plans of fire services across the country.
Meanwhile, the work the council carried out with the Building Research Establishment has formed a blueprint for other housing providers nationwide.
Cllr Crane said: "The regeneration projects have taken the council into uncharted territory which, while presenting many challenges, has also provided opportunities to innovate and inform the work of fellow councils, housing providers and the emergency services who have responsibility for high-rise accommodation.
"We have welcomed the support from the fire and rescue service, social housing providers and other stakeholders to help us ensure the welfare of our tenants, support which has underlined the benefits of collaborative working."
All tenants at Biart Place were rehoused in council, social or private accommodation within eight months of councillors rubber-stamping the site's regeneration plans in April 2018.
The decision to regenerate Rounds Gardens was taken in February 2019, and the council has already helped 100 households find a new home and remains on target to fully decant the site by March 2022.
Throughout the decants of both sites, council officers have dealt with each household on a one-to-one basis, discussing housing needs and drawing up a tailored plan to find the tenant a suitable new home.
Tenants were also kept up-to-date with decisions on the future of the blocks, receiving hand-delivered letters both before and after meetings where key decisions were made on the future of the sites.
Create Streets, an organisation focused on creating attractive and socially successful communities, was brought in to help understand community aspirations for the sites.
Cllr Crane said: "While we were aware of the need to act quickly and decisively in determining the future of Biart Place and Rounds Gardens, we never lost sight of the fact the tenants had to be at the heart of the decision-making process.
"As a council, we were presented with a significant challenge, but we have always remained acutely aware of the uncertainty and upheaval our tenants have faced, and the need for us to place the welfare of our tenants at the top of our agenda."
Cllr Crane added: "While we're obviously very pleased to have made the shortlist for the Council of the Year Award at the UK Housing Awards, we know the hard work has only just begun when it comes to delivering these regeneration projects and building modern council homes for our tenants and affordable housing for our residents.
"However, what we have achieved so far shows we're ready for the challenges which lie ahead and can successfully finish what we've started."
The 24th UK Housing Awards, organised by the Chartered Institute of Housing and Inside Housing magazine, take place at London's Grosvenor Hotel on Thursday 7 May.