Titanias some councils do offer 'healthy eating' courses that include basic cooking classes, ask your council.
If you consider when 'proper' cookery lessons stopped and when we started getting problems with child obesity there is a rough correlation (yes I know correlation doesn't prove causation and that's not the whole story I think common sense lets us realise it's a factor).
Ditto the increase in food waste, popularity of takeaways and debt I think is not unrelated.
As for schools couldn't fit it into timetables - why not when it was done in the past? I went to high school on the 80's and did the following subjects
Maths - financial education can be included here
English
Biology - nutritional education here
Chemistry - little more nutritional ed here
Physics
History
Geography
Sociology
French
German
RE
PSE - this included sex ed, rights and responsibilities,
PE
Home economics - included cookery basic cheap nutritional dishes like soups, lasagne (including pomodoro and bechamel sauce from scratch), cottage pie, 'normal' pies, curry, stew/casserole, basic cake recipes (sponge, scones, flapjacks), budgeting, meal planning.
Textiles - we all had to make a skirt and yes girls only then
but in the process of making a skirt we learnt how to fit a zip, sew on a button, do a hem...
We just didn't do all of them every term eg a different science per term, or switching at half term, then at end of 3rd year we selected options according to what exams we wanted to sit.
Yes ideally parents should be teaching but I'm certainly aware of too many parents who would have been teens in the 90's when home ec was done away with in many schools, who can't cook can't make even a basic sauce even from a dried packet! So as they don't have the skills they can't teach THEIR children.
It may not be right but it's where we are and as the consequences affect our economy and health as a society it's all of our
Problem.
I do think that one thing that HAS to come from parents is not STOPPING children from doing things at home. It's honestly not going to kill high school age children to boil kettles, use hobs, ovens and sharp knives yet I hear so much about children my daughters age (almost 16! So in theory almost old enough to be mothers!) not being allowed to even make a cuppa in case they hurt themselves. Ridiculous!