Hi Dan,
Sounds like an interesting idea - are you thinking of Primary or Secondary? State or private? Parents to pay or schools to pay?
There's someone who tried to do a similar thing at our (state) Primary - she was going to wrap it around Yoga - mostly stretching and exercise with some nutrition. I'm not sure if any mums took it up - I guess it depends on the geographic area, type of school, parents involved - this lady was passing on the cost to parents - £5 per child for a lunch time club, weekly.
I don't believe it went ahead as I guess parents in our area didn't wish to pay or were into healthy eating and exercise themselves. I didn't take it up as our family is very much into exercise and healthy eating and I teach my kids how to prepare this type of food at home.
I would consider looking at the obesity side of things - I think the UK now runs camps for kids struggling with size issues and this may be where you could find work - but it would be in the holidays.
Otherwise I'd say approach private schools and see if their parents are interested first - parents in these schools may work all hours (to pay the fees!) and may not get much time to do exercise or teach their kids to cook...(vast generalisation here) but mostly they may have the spare budget? No idea but I'd probably try private first as this would give a good indication as to whether parents would support it financially...
I'd be looking at teaching healthy cooking actually - state schools do this really well - but I'm not sure if private and independent schools still offer Home Economics or cooking as their timetables may focus on more academic subjects only - so they might be interested in a healthy cookery club? Again, vast generalisation but you could do some research?
Best of British!