The buildings in Shefford High Street were home to the former Shefford Laundry until it was bought by Tesco more than 15 years ago.
In the time since there have been reports that the firm was considering opening a new store at the site, but it has remained vacant.
Shefford Town Council and Central Beds Council have also said that the buildings have fallen into a poor state and want Tesco to take action.
Central Beds Council has said that if Tesco does not act it may have to serve a Section 215 Notice – under which the company would be legally obliged to improve the buildings.
Shefford mayor Councillor Paul Mackin said: “We make every effort to keep our town centre in a decent and presentable state and it is a disgrace that Tesco can neglect the site like that. Like Central Beds Council we have written to them and we have also invited a representative to come to our council meeting in January – though I’m not expecting anyone to come.”
Councillor Nigel Young, executive member for strategic planning and economic development at Central Beds Council said: “The buildings in Shefford have been in an appalling state for some time and we are as keen as Shefford Town Council to get them to an acceptable standard.
“We have written to ask Tesco to improve the appearance of the buildings, which is the very first step in taking formal Section 215 action against them.
“We’re hopeful that we won’t need to go much further down this enforcement route, but we have that option available in order to get it sorted.”
A Tesco spokesman confirmed that the firm will take action. He said: “We have arranged for works to the exterior of the buildings to take place in the new year to make sure that the site looks better for the community.
“This will include fixing up the outside of the buildings, replacing any broken windows and generally making the site look more tidy.”