Is it worth remarking my GCSE’s

Honestly, it's not likely. You would have to ask the school to download your papers, then ask one of your teachers to review them. This is their holiday, remember, they would be doing this in their own time without extra pay. Then, if they thought you had been marked unfairly, the papers could be sent for remark. There is a fee per paper, not per subject, so you or your parents would be asked to pay this. And marks can go down as well as up.
A 6 is not a bad grade. Your sixth form is being a bit harsh to insist on a 7. You obviously did history and geography; it is a bit unusual to do both. That is a lot of content to learn, and that is possibly why you dropped a few marks. What were your English grades like? If they were reasonable, your best bet is to write or email calmly and persuasively to your new head of sixth form and history lead, explaining why you want to do history, why you have the skills to ensure you get a good grade and what you are going to do in terms of extra reading etc to hit the ground running. Hopefully you will persuade them.