Extra cash is being given to a secondary school to help it expand and take on more pupils because of high numbers of children in the area.
Wakefield Council agreed to hand Kettlethorpe High School in Sandal around £3.6m in July 2017 for it to build extra classrooms.
The school will take on an extra 30 pupils per year from September next year in a move which will eventually see its overall capacity rise from 1,600 students to 1,750.
But now the local authority has had to plough an extra £900,000 into the expansion because of a late change to the designs after English Heritage objected to the original proposal.
As a result, the cost of the work has risen.
In a report which went before the council's Cabinet on Tuesday, elected members were told that school place pressure in the district "needs to be addressed".
It added: "If the option at Kettlethorpe High School is not progressed another option will need to be explored, but the places would not be provided within the required timescales."
It also warned that if the project was abandoned then the council would have to pay to terminate it.
Councillors unanimously agreed to release the extra funding.
Portfolio holder for children and young people Margaret Isherwood said: "There is pressure on school places. It's very important that we have Kettlethorpe expanded in this way."