According to a writ filed at the Technology and Construction Court in London, a dispute over their contract arose over the summer and was taken to adjudication in August.
After failure to pay, PT Building took its claim to the High Court and was this week awarded £314,000 plus costs.
The contract had principally included work to fit out kitchens and bathrooms under the council scheme. Rok has until 22 December to pay the sum.
A Rok spokeswoman said: “Naturally we are disappointed with the result and the judgement rejecting our submissions.
“We took counsel’s advice before embarking on this course of action and were advised that we had legitimate concerns about the quality of the adjudicator’s decision and that there was merit in taking this to enforcement.
“However, at the hearing the judge preferred the submissions of the claimant.”