You Don’t usually do anything to accept the Firm or Insurance on UCAS.
So if you are declined by the Firm (and remember many places will accept a near miss anyway) you can make direct contact with them to tell them you’re putting in for priority remark and will be in touch in a few days if the mark goes up.
The uni websites tell you about sending them evidence of upgrade and then UCAS position can be changed to Unconditional for what was the original Firm.
In the meantime whilst waiting, the Insurance remains the unconditional offer. This will be the case until you have evidence of a higher grade that meets the old firm offer. You can hold off any communication with the Insurance whilst waiting. Or if you do have to fill in any forms etc, if you are re-graded they will release you anyway on a regrade.
The thing is, unis make a contract when they give you an offer and if you’ve firmed them they are obliged to take you if you meet their conditions, even if only on remark. So this also means the insurance must release you. In fact, the student is free to pull out of any of it if they wish to.
I guess the only thing you might want to be careful of is paying any accommodation money to the insurance whilst waiting for a review of marking. It’s unusual for there to be an immediate allocation of accommodation - usually takes a few days - and students are usually given a week to make the deposit payment anyway. It might be different with private accommodation, so you’d need to be a bit more careful.
Priority reviews put in for on Thursday if results day, have been known to come back before the weekend or more commonly on Monday or Tuesday. They go to the exam centre-school or college and the exam centre has to make the request. So if putting in, do ask the school or college if staff will be in daily and forwarding info about review results as they come in. Try to get a number and name of someone you can follow up with as you don’t want the review results languishing on an inbox of a college or school, but to quickly be passed to you.
Reviews of marking can be worth it if the mark seems v out of kilter with expectation, especially on one paper. It’s best only done if the student is close to the grade boundary above and not close to the one below, as the risk if marks going down and resulting in a lower grade, is clearly higher. Sometimes teachers will think there’s something analogous in the marking of the whole centre (if the centre has been marked by 1 marker - less common these days) and encourage several to put in for a review. But in the end the student must choose.
There is a cost - maybe around £75 for each paper for priority review as it’s turned round so fast. But it’s refunded if the grade changes. Most don’t, but a sizeable proportion do - maybe around 20%…usually because it tends to be those who really were expecting better and whose marks look odd who put in for reviews. General speculative reviews are less common because of cost and risk and if there were more, the success rate would probably be lower. But sadly marking isn’t foolproof.