@Pebblepoppy
Why would you want a break? Yes, technically you should have one if you work over 6 hours, but it would be unpaid, so if you have a 30 min break, you'll be at work for the same amount of time, but paid 30 mins less.
If you really want it, yes you should have it but ime, people working those kind of hours prefer not to.
Are you having a laugh???
'Why would you want a break?' 🙄 What kind of question is that?! Six and a half hours with no break is not on. OP should have a 15-20 minute break, (minimum) to have a drink/a bite to eat/a rest. About 3 and a half hours into her day. Probably around 1pm to 1.20pm... And she should get paid for it!
How ludicrous to suggest she shouldn't WANT a break! 
I always offer a break to my people working slightly over 6 hours. They never want it.
And 'your employees' don't want a break after you have graciously offered one after six hours! Why on earth not?
They deserve one. They need one. You should GIVE them a break, not ask if they want one. With the attitude you are displaying, it sounds like they would be afraid take a break!!!
Another thing is, you claim that people don't need a break after 6 to 6 and a half hours, yet you say you offer one. That's not making sense to me. Why would you offer them a break after 6 to 6 and a half hours, if you reckon they don't need one?!
Good grief, no wonder so many people hate work, hate their bosses, and have so much sick leave, and work related stress! Some employers are not employee friendly! At ALL!
@MsAdoraBelleDearheartVonLipwig OP you need to get this sorted, and report your employer if they refuse to give you a break. Or as you said, find another job. Your employer sounds dreadful. Contact Citizens Advice or ACAS. If you let employers get away with treating you badly, they'll keep doing it!