John Grantham, who has campaigned against the development, said the latest news was a disaster for the town.
He said: “The council now admit they’re now looking for an unbelievable extra £2million.
But it’ll never just be £2million more. The council’s track record on the project is appalling.
“It’s a catastrophe and exceedingly painful for all, including and especially surely those who’ve bull-dozed this white elephant project through to date.”
He said the council should now abandon its move to Charles St and an independent survey carried out to find a cost-effective use for the offices.
“Whatever is proposed must first be put in a town poll to all residents of Dorchester, then by referendum to all residents of West Dorset. But this time the public must have full, proper, detailed information, and be able, by voting, to express a view binding on WDDC.”