No teachers don't earn overtime, and I'm not sure it really balances out over the year. The 1265 hours we're directed is when we are told we need to physically be somewhere, in front of a class, in a meeting, in a parents evening, on duty etc. It includes hardly any of the time needed to actually do the job. The vast majority of the time needed to plan, mark, respond to emails (oh the 1000s of emails), contact parents etc is not accounted for in our contracted hours, nor is it paid as overtime, nor as time in lieu. The holidays are long, but I'm not sure an extended holiday quite makes up for the 50+ hours regularly worked a week in term time. It's not like my family exist in school holidays only, they're there all year and my kids need their mum all year.
But I digress, on to the lunchtime issue. Yes, hundreds of teenagers do need supervision during a lunch break. Yes most are perfectly well behaved, but a minority are not, and that minority need adult supervision. I'd love a 45 min lunch break rather than 30 minutes, but we have found that we have less issues with behaviour when it's only 30 minutes. Plus we don't have enough space for them at lunch, extending our current buildings is another thing we have no money for, so we actually have two lunch breaks to accommodate them all (teachers are in timetabled lessons when not on their half hour lunch break). Schools are so short of money, I think everyone knows that, but Academies aren't really the problem (although CEO pay doesn't help, we didn't have CEOs before schools were Academies), chronic, sustained underfunding over more than an decade by the current government is the problem. Adding any extra time to the school day, whether it's at lunch or at the end of the day or whenever, costs money so it simply can't happen. Whether you believe it or not, any extra time when students are in school needs adequate supervision, and it needs the site staff and appropriate support staff on site, and the lights and heating on etc. And it needs enough space for those students to actually be somewhere, if not in a lesson with a tracher. So a longer day is impossible at the moment I'm afraid, with funding as limited as it is.