I wouldn't put much trust on the league tables. They rank St Andrews absurdly high in most subjects, and universities like Imperial,and Manchester which are very well known and competitive for computer science are ranked below relatively obscure unis like Aberdeen and Stirling. Edinburgh is ranked 23th on the complete university guide when it has the highest research output in CS and is a top employer choice. I would say that, in terms of prestige for Computer Science, these are the most well known universities in the UK:In order of ranking. These unis are all prestigious, and have competitive UG admissions for CS.
Kings College London