Headteacher Margaret Nicholls remembers one high-flier from last year who gained a place at Oxford but turned it down. "She said that it was not for her. She had done it for the school and to prove something but opted for Manchester University instead," she said.
"This is what we are up against, trying to convince pupils that they can break the cycle of underprivilege and underachievement."
The city is considering putting Wood End estate, which is partly served by Woodway Park, forward to become an action zone. In some streets 80 per cent of adults are unemployed, compared with about 11 per cent in the area as a whole. Senior teachers, who visit the homes of all new pupils, report houses with little or no furniture and children living in overcrowded rooms.
Almost one in three of Woodway Park pupils come from lone-parent families compared with 16 per cent overall in Coventry.
Many GCSE pupils at the school have Saturday jobs and almost every sixth former works part-time in order not to be a drain on their families' limited incomes. Some of them supplement the household budget.
Mrs Nicholls said: "These children need support. They are the first in their families who are staying on to go into further or higher education, but they bring all manner of problems into school with them.
"The Government should rename these zones 'community action zones', to reflect the intakes of schools such as this. The scheme should involve setting up youth clubs and other activities out of school. I would also like to see more direct help being given to families."
Mrs Nicholls also has reservations about devoting more time to literacy and numeracy at the expense of other subjects, as ministers have suggested. "We have to be careful about possibly disenfranchising children from the national curriculum, to which they have an entitlement,'' she said.
The city council is poised to put forward a proposal for an education action zone as soon as ministers have set out their thinking on the issue. It believes the policy will tie in with work already being done in the city.
Chris West, the education authority's resources manager, believes there are three or four parts of the city which might qualify to become action zones because of multiple deprivation factors - the worst affected being Wood End.
He said: "It all boils down to is motivating people in communities where there is despair and making them feel empowered. We are waiting for the Government to tell us what it is we have to do under the action zone proposals."