Most top univerisities (such as Oxbridge, Imperial, UCL, York, Kings, Bath, Manchester, Southampton, Nottingham, Bristol etc) will require either Maths, Statistics or Physics for their Computer Science degrees.
However, there are quite a number of universities that will accept your Computing A-Level for their computer science degrees, such as Kingston, Brunel, City, Oxford Brookes (to name a few).
Another alternative for you could be to do a degree in IT or similar, instead of Computer Science. For instance Queen Marys does a degree in 'IT in Business', and Southampton has a degree in 'IT in Organisations' and there are several others, which im sure ull be able to find on the UCAS website.
The maths required for a computer science degree is tough, especially at top unis, therefore you might struggle if you dont have a mathematical background. In the first year you will cover many aspects of A-level maths, such as integration, binomials, vectors, induction, trig functions and differentiation - which will then be followed by very intensive logic and discrete maths.
However if you are willing to work hard, then the maths shouldnt be a problem, but it will definately be an advantage to have A-Level Maths or a physical science.