Any advice? (UCAS Preds)

Hi, I recently have gotten my UCAS predicted grades for my subjects which were BBB. I study Maths, Economics and History.

I am wondering whether to ask my teachers to give me an assessment to do in order to change it a grade higher so I can send off my UCAS application quicker. I have mock exams at the end of November which can also help my grades however, I'll be getting the grades for them around December time which could be too late.

Shall I try convince my teachers to give me an assessment soon in order to prove myself or wait until the mock exams and ace them with high grades but sending off my application a bit later?

My economics teacher is setting a test if you believe you want your grade to change so I'm going to try it for my Maths and History teachers. I would like my UCAS grades to be AAA-A*AA in order to do an Economics degree at a Russell Group university. I would've hopefully done well at the end of Year 12 mocks back in June however COVID-19 affected it massively. I can only try prove it now and try get the top grade but I'd like some assistance from people who've applied for a Russell Group university around December and have been accepted or just any advice please, thanks.

No matter how you approach it, the key element will be your Maths prediction.

I think I can get A* predicted. I just haven't had any big exams recently for them to determine it