It is possible, although not usually advised. Some universities do not like to consider applicants at other universities. If you are going to retake some modules it is usual to retake via your school, as you will need new predicted grades, and possibly a new reference.
You should not lie about what you are doing, as if this comes out at a later stage, your offer could be withdrawn (up to and including once you are attending the university, so you would have to lie about how you spent your "gap year" for a full three years). You would also be asking your referee to lie for you, which they are unlikely to want to do.
It will be difficult to retake A levels alongside doing the first year of a university degree and achieve your potential in both of them. What if your exams clashed? Many university exams take place at a similar time of year to A level exams. It would be best to make a decision now as to whether you want to improve your grades and take a gap year, or commit to the place you already have.