If you look at their websites you will see what their GCSE requirements are. Most unis have minimum requirements in GCSE Maths and GCSE English language, and I believe most of those expect a 5 or above. I would recommend aiming to retake those GCSEs, particularly because even outside of university, quite a few jobs look for the same requirement as those two GCSEs are used as standards for literacy and numeracy. If you get 5 or above in those as resits though then they generally won't have an issue - GCSE resits are much less of a concern for unis in general in those two subjects.
The A-level resits may be a concern for some unis, although many will consider applicants who are resitting in a gap year. Given your background of disrupted education etc, as well I suspect stronger attainment now would be viewed positively relative to weaker attainment when you had other personal challenges ongoing. Your academic referee should explain the situation in which you recieved those grades though i.e. about sleeping rough and working to support parents and other family issues and so on.
You may well be eligible for a contextual offer too given the background, although note that usually contextual offers still require you to meet an GCSE requirements! They might just give you a lower A-level offer.