But most don't want to. Nic Barnard reports
When politicians start offering parents a greater choice of schools, a general election can't be far behind. The bidding war for the parent vote started early this year - at the North of England education conference.
There, the new Education Secretary Ruth Kelly proudly boasted that Labour was "allowing popular schools to expand more quickly and more easily".
The Conservatives hit back with their own "right to choose" policy to let successful schools grow - making it the third election in a row they have made the pledge in one form or another. It has not yet won them power, but Labour clearly thinks it is enough of a vote-winner to be worth nicking.
It is well over a decade since the Conservatives began to liberalise the school admissions system and introduced the idea of parental choice. It's also nine years since the Audit Commission concluded in its Trading Places report that "genuine choice (did) not exist" for most parents.
The quest since then for both main parties has been to find ways of creating a genuine choice of potential schools for parents. One idea, too obvious to ignore, is to let good schools grow.
The immediate stumbling block came in the form of surplus places. Local authorities have spent a decade stripping them out to cut waste, and empty desks in one (struggling) school have been the main reason for refusing to let another (popular) school grow.
But now the Department for Education and Skills has scrapped that rule. Any successful school can put forward a proposal to expand, and there should be "a strong presumption" that this will be approved. The DfES even offers a capital grant of up to pound;500,000 to help them grow. A fast-track process to grant permission in less than 12 weeks is planned.
Education authorities are told to consider how to "tackle the consequences" for other schools, but that is all.
Upping the ante, the Tories propose a School Expansion Fund to provide 600,000 extra places at popular schools - equivalent, they say, to 260 new secondary schools, ensuring 100,000 extra families would get into their first choice.
But would it? Labour's cash incentives have hardly prompted a dash for growth. Only 14 schools have so far bid for grants, and just nine have been approved.
A TES survey last month of some of the country's top comprehensives helps illuminate the low enthusiasm for expansion. Two-thirds said they would not expand, and only one in six was definitely considering it.
Many headteachers said they simply did not have the space. Others said they liked their school the way it was - and that the parents did too.
Joan Olivier, head of west London's Lady Margaret school, with 570 pupils, said growing much larger would "kill the goose that lays the golden egg".
Significantly, many heads were opposed in principle because of the impact on other schools. They fear expansion of popular schools will turn others near them into sink schools, stripped of pupils and resources. It is at these schools that the most vulnerable and challenging children inevitably land. A number of church school heads even considered the policy "un-Christian".
In a double whammy, pupil rolls are expected to fall over the next decade, increasing the chaos.
Dennis Richards, head of St Aidan's CE high school in Harrogate, said:
"It's an aspect of competition that I think has got out of control. It's not a policy I would expect this government to be associated with."
David Hart, general secretary of the National Association of Head Teachers, agrees. He dubs the policy "the devil take the hindmost" and says those who advocate it have never been able to explain "what to do with the pupils and parents and staff in the schools that are simply withering on the vine".
The policy also flies in the face of other government initiatives, points out DiAnne Smith, head of the oversubscribed Admiral Lord Nelson school in Portsmouth. After years persuading schools to collaborate, ministers now seem to want them to compete again.
Schools in Portsmouth have grouped themselves into the Portsmouth Learning Community, and Ms Smith says: "Collaboration is at the heart of what we do.
I'm not just head of ALNS - I'm concerned about all our schools."
What's more, encouraging children to travel miles to school seems to conflict with plans, laid out in the Children Act to build "extended" schools that would be the hub of children's local health and social services. Heads will be strongly encouraged to forge close links to other services.
The result, she says, is that schools will need to be more closely rooted than ever in local communities. "It doesn't make sense that children travel long distances just to get to a popular school."
One fear among sceptics is that too much expansion will create over-sized "super-schools" - impersonal institutions where behaviour runs out of control and results start to spiral.
But a review by London university's institute of education of existing research into school size refutes these "prevalent myths" that large schools underperform.
The research base is scant, but the review tentatively suggests an optimum size for secondary schools of around 1,400. Pupils and staff might be more comfortable in smaller schools, but that doesn't necessarily translate into better results or behaviour.
So could more be done to persuade schools to go for growth? On top of the cash, the Tories suggest easing the planning laws to allow schools to squeeze more classrooms onto crowded sites - by adding an extra floor, say.
The think-tanks also have ideas. Philip Collins, director of the free-market Social Market Foundation, says more heads might consider expanding if they got money up front - at the moment, budgets are based on pupil rolls from the previous January's census.
They could also respond more quickly to rising demand if parents applied for places earlier - say a year ahead. But what if applications fell the next year? Collins argues the cost of keeping open an empty classroom is "negligible" but adds: "If demand falls because a school isn't doing well, then good. Who in the end are we really worried about? The providers or the pupils?"
But for the policy to succeed, popular schools are going to have to want to expand - and that is far from certain. Even the Tories finally admit to crucial question marks over their market-driven policy. "You can't hold a gun to anyone's head and say 'You must expand'," Tim Collins, the shadow education secretary, admits. "It's something of a leap in the dark. This is something no G7 country has taken on board as policy."
And here is one final reality check, to be found in the Tories' own Right to Choose document: Thomas Telford school, in Shropshire, one of England's most successful comprehensives, last year had 1,286 applicants for 168 places. Even if it doubled in size, there would still be 1,000 disappointed families come September.
Still, there is an upside: by then, the election should be long past. Just don't tell the voters.
For three years now, Fairfield high school in Bristol has taken an extra class each September.
It's one of the first to benefit from the Government's fund to help popular schools grow. But it has not been easy. Governors decided on expansion only after being confronted with the prospect of having more pupils imposed on them by appeals to this oversubscribed comprehensive.
And there is more to come: from September, Fairfield will almost double in size under a city-wide reorganisation. A new school is being constructed.
"We only anticipated taking an extra form for a year, but we've done it now for three, so we're running a much more congested site," headteacher Nicky McAllister says.
Much of the playground has been lost. Lunch is now a double shift, to the delight of senior staff on lunch duty.
Meanwhile, there are new staff, including newly-qualified teachers and graduate trainees, who inevitably need extra support. "Children like stability, so obviously over-crowding plus taking on less experienced staff has a knock-on effect," Mrs McAllister says. There are more "squabbles" in the playground.
Planning for the move to the new school means the head is often off site, putting an extra burden on her deputies. A consultant is helping draw up the "nightmare" timetable for next year, when the school will be split-site. "The further we get into it, the more problems crop up," Mrs McAllister says.
But the biggest questions are over school structure. Many decisions will be delayed until all the staff are recruited and can have a say.
"A small school is great - you know all the kids. But how do you structure a big school if you want to keep the same ethos?" she asks.
"We keep in mind the big picture of what we want in the end, but work towards it in bite-sized pieces.
"It's been a huge learning curve."