But in March, after five months of viewing schools and filling in forms, they were told there was no space at any.
Instead, Jack was offered a place at another nearby school which was in special measures and where bottles had been thrown at the couple when they had gone to look around.
"What we found out was that the 'choice' which Tony Blair had talked about didn't exist," said Mr McGuire, 36, a tour manager.
"All we wanted was a good, local school. Instead, all we were offered was the one school in special measures. The whole thing was ludicrous."
After appealing unsuccessfully against the local authority's decision, Mr McGuire contacted his MP, wrote to the local press and ended up challenging the Prime Minister live on Radio 2.
"All this choice is a smokescreen to cover the fact that after Labour's eight years in power, schools are still failing," he said. "Some are good, but the bad ones are out of control. How can you offer choice with that?"
Jack, who is now 11, was without a secondary school place until July, when he was offered a place at Deptford Green school in Lewisham.