If you want a list of universities that don't have Further Maths as an unwritten requirement, might I suggest Durham (28% of people who get into the CS program don't do Further Maths), Edinburgh, Manchester (where they only care about getting 3 A*s but with one of them being in Maths. I know this because that is what they said at the Open Day. The only problem is several offers have already been given out for CS at Manchester and so there will be increased competition for the remaining offers, though there are still lots to be given out), Bath (Maybe) and there are a lot more.
Also, might I say that I don't recommend applying to Warwick? One of my friends went to the Open Day and the facility is extremely small (unless this is what you are after, in which case, 100 % go for it). It was about 1/5 of the size of the Durham facility and they dropped significantly in the rankings because of the loss of funding from GCHQ (I got this info from my CS teacher).
What I will say is this, you don't need CS or FM to do Computer Science at uni. The fact that you have achieved these grades already puts you at an extremely advantageous place compared to other candidates as you have already met their minimum entry offer whereas it is still in doubt for the other candidates (like myself) applying with predicted grades and through doing only STEM subjects, you have put yourself in an advantageous position even more so.
However, you have only got three subjects compared to the majority of applicants at the top universities that do 4 A levels so there is a plus side and a downside so the only way of knowing whether you can make the top universities is to apply to a mixture of universities and then see what offers you get back.
University doesn't matter too much when it comes to jobs. Obviously, it will be taken into consideration as it shows signs of aptitudes but if you show higher aptitude coming from a middle-tier or a low tier university than someone who is middling in a high-tier university, chances are you will be employed over them.