As others have said, unfortunately when you're applying for a course with 10+ applicants per spot with the vast majority of said applicants meeting all the basic requirements, there is no reason for them to make an exception. I would resit the ones you need as soon as you can, even if it's not this summer - generally I'd aim for 7s in English, maths, biology and chemistry (+ one other 7, and if you can get it in physics then great) as that means you should be able to apply to pretty much every uni, giving you the most chance. You could try emailing the unis to ask directly if you have any extenuating circumstances for your grades, but unfortunately I wouldn't really expect them to make exceptions. Additionally, you could look into gateway courses if you are eligible for them, but bear in mind most unis only have like 20 spots for those so it may be even more competitive and you will need to meet the criteria.
As for your question about grades being higher if you apply after Year 13, that's not strictly true. All unis have different requirements so you would have to look those up, and if unsure you can always email the admissions team. If you are applying for the first time to any uni without any A Level resits, you'll have the standard requirements. I don't think GCSE resits apply but may be worth checking, particularly for the Scottish unis as they are a bit stricter on resits (they don't accept resits for A Levels). For Liverpool if you resat an A Level the grades would go from AAA to A*AA, but again I don't think that counts for GCSEs. Applying say after a gap year but not resitting any A Levels does not increase your grade requirements. Some unis only accept 2 application rounds which may be something to bear in mind when choosing options - i.e. applying 'on a whim' to see if they may make an exception when you don't meet requirements and you haven't contacted them about it may not be totally risk free.