Police are still appealing for witnesses to the fire which tore through Willow Place multi-storey car park after news it will cost at least £1m to repair the damage.
Contractors have started work on the main car park and on a cellar area, where the blaze started.
It is hoped the car park will re-open soon.
Police say the fire, which started in the early evening of Tuesday, December 30, was started deliberately.
At the height of the blaze fire crews from Corby, Kettering, Daventry, Moulton, Thrapston and Burton Latimer plus crews from Leicestershire were at the scene.
Seven people have been arrested in connection with the incident including a 12-year-old boy, a 13-year-old boy and two 14-year-old boys.
All seven people have been released on bail pending further inquiries.
No-one was hurt in the incident, although one person was treated for minor smoke inhalation at the scene.
Police would still like to speak to anyone who may have been in the area of Willow Place on Tuesday evening, shortly after 6pm.
Any witnesses to the blaze can call Northamptonshire Police on 101 or they can talk to Crimestoppers anonymously on 0800 555111.
Town centre manager Dan Pickard said: “We think it will cost £1m to repair the damage caused by the fire.
“That’s a ball park figure based on the figures we have available.
“We will know more after the site meeting with the structural engineers.
“At the moment we are clearing up the car park, the bigger job is clearing up where the fire started then we can see what needs doing to the electrics and the steelwork.
“We hope to open the car park again in two weeks.
“People in the town have been very supportive and general footfall is above the national average. People are supporting the town which is really good news.”
The fire forced stores including New Look, River Island, Dorothy Perkins, Burton and Evans to close due to smoke damage.
Evans, Dorothy Perkins and Burton only re-opened on Thursday, January 22.