Resitting A-levels a disadvantage for Imperial/UCL/Edinburgh

Whilst I don't know about the specifics for your mentioned universities, I re-sat A-levels and applied for (notably) KCL, Durham and Exeter.
Most universities will say that you should include 'extenuating circumstances' (EC) in your application to explain why you are re-sitting. By the sounds of it, you don't have any. I was the same - I was re-sitting as I didn't feel my A-levels reflected my ability. Hence, I didn't include any EC's in my application. Despite this, I received offers from Durham, Exeter and the rest of the universities without them asking for any other information.
However, KCL instantly and automatically rejected my application. I emailed in asking why, and they explained that they automatically reject candidates that are re-sitting A-levels, unless there are EC's. Unfortunately, I would imagine that Imperial is similar to KCL, although this is just a hunch.
So, I would advise you email ahead to the universities you would like to apply to, asking explicitly whether it will result in automatic rejection, if their policies are not clear on this, but do not be put off if they tell you to include EC's.
I should also mention that I was applying to read a law degree, which required a standard entry test (LNAT), so the universities did have another useful metric to decide my suitability. If you are applying to a course that doesn't have any entry tests, you might not get the same results.
Ultimately, I would suggest that you consult both your current institution (because surely they have previously advised on this) and also the universities you would like to apply to in order to get further information. Further, I would advise that you seriously consider re-sitting your exams if you have already achieved excellent results (such as AAA+), especially if you are not able to prove your capability through something like an entrance exam or interview, as - being as realistic as possible here - you are competing with candidates that, on paper, appear simply superior.
Hope my experience in this can be useful to you and I wish you the best in whichever path you take.