Aj12 is right here. Having worked at a uni for a while and seen this from the inside it just doesn't happen. You hear stories on TSR so some people will convince themselves that it is viable, fair enough, but prepare to be disappointed on the day when you try and beg your way in and just get stonewalled from the university.
The university gets your grades on the Sunday before the Thursday they are released, in most cases there is a bit of a shortfall in people who actually make their grades (but in a year where there are lots of applicants it is very tight), ie a course may have 30 places on the quota for UK/EU students, they make say 60 offers, end up with 40 accepting as firm, and 25 of them have made their grades which leaves a shortfall of 5. Over the days between Sunday and Thursday, the admissions tutors will be going through the UCAS forms of the 15 who missed their grades and will choose 5 who they confirm anyway (usually the 5 best of the ones who just missed by one grade).
But one thing that has come in recently is increasing quality in Clearing, there are lots of applicants that applied for competitive courses and ended up with no offers, or declined as they wanted to change course etc, and have AAA or AAB in Clearing, so if the uni wanted say ABB grades and have a shortfall, they might choose to confirm the ones who got BBB, but rather than accept people who were 2 grades down that they had made offers to, they will just go into Clearing with a shortfall and easily pick people up.
The quota rules are strict, if the university exceeds its quota there is a fine of about £10k per student. There is a little bit of flexibility within subject areas, eg if you underrecruit by 2 on Economics and Geography and overrecruit by 2 on Economics and Politics they aren't going to fine you, but it is quite a delicate game and one that will leave Heads of Department super stressed on results week because they will get hauled over the coals by the Chancellor if their department ends up causing the uni a fine, and so admissions tutors are always worried about getting hauled over the coals by Heads of Department.
What a lot of 6th formers don't understand IMO is that the university has had four days before the results are officially out, to consider whether to confirm those that missed their grades or not, and they have decided the ones to confirm and fill up the places. A good rule of thumb for whether you can make a case to get accepted is, is that course in Clearing? If it is in Clearing and you originally had an offer then it means there are places so you might be able to get in. If you missed your grades and they haven't confirmed you and they aren't in Clearing that means the course is full and they will be fined for exceeding the quota so you won't be able to talk your way in.
Now I know that for students who are in that situation and desperate to go there they will try anything no matter how remote the chance, so there is one long shot strategy to bear in mind. Every now and then you get people who met their firm, who decide late on that they want to go on a gap yah to Burma, and ring up and ask if they can get deferred. This is a pet hate of admissions tutors especially if it happens a couple of days into clearing because they think they have their numbers tidy but then if they let one defer they have to replace them and might not be able to at that point. So if you are in the situation where you had a firm offer, missed it, and they didn't confirm you, it may be worth giving them a call saying you understand the situation and that they are currently full for numbers, but really want to go, and you'd like them to put you on a reserve list in case any students wish to defer. This might sound a long shot but it could happen....because if someone does ask to defer and you are on their list and managed to convince them that you are a mature and sensible person, they might think fair enough let gap yah kid defer and we will take them.
Not sure how viable that will be this year, if people defer they will probably face the higher fees, but this is the only realistic strategy I can think of.
On results day the admissions tutors are really stressed and busy and their biggest hate of all is when they have spent 4 days agonising over who to let in that missed their grades, and got their numbers sorted, to have to field phone calls from all the people who say "I was LITERALLY 2 marks off an A and am getting it remarked" (the answer will be, well until its remarked its still a B), or "my Nana died and I suffered depression during the exams" (the answer will be, this should have been raised to the exam board at the time). You would not believe how many try these excuses on, there will be one every 10 minutes on the Thursday of Clearing, Admissions tutors will often tell the people staffing those Clearing lines (who are usually undergraduates doing summer work) not to put any of them through, so it just makes them feel bad, having an 18 year old girl in tears on the phone begging. I had a girl say she thought her life was over, all her friends had got in, her parents were shunning her, she just wanted a chance to make up for botching one A level, and it feels bad because you can't do anything, but in that moment the person on the other end of the phone is desperate and doesn't know where to go for help.
The other thing I found is that Admissions tutors often have a cynical attitude towards people who have excuses for not getting their grades, as one told me one time - the ones who do that are the ones who will always have excuses and special circumstances appeals when they are at uni and get a 2:2, and tutors hate all the admin and having to tick all the boxes to show they have treated the student fairly, when that happens, so they won't touch those students with a barge pole.
It obviously depends on the uni and how competitive it is, if the demand for the course is low then you may have a chance, as I say, the best guide is if that course is in Clearing or not, if it is that tells you they have not filled their places. If it is not in Clearing then you are just going to be banging your head against a brick wall because the uni will get fined for exceeding its quota and you will just end up talking to someone who is not allowed to take you and will feel bad, although after a few hours worth of hearing the same excuses you do tend to harden up. You are better using your time phoning round other unis who are in Clearing rather than getting more and more frustrated when you just get told no.
Well thats my advice anyway, I'm sure loads will try it because they are just desperate to get in their firm and I can understand that, but if you do, don't have high expectations.