Generally speaking, yes - the rule of double jeopardy / autrefois acquit would prevent that person from being tried again for the same offence. However a new law was brought in around 20 years ago which meant that for some serious offences (murder, manslaughter, rape, and some others), a defendant who had previously been acquitted could be tried again for the same offence where there was ‘new and compelling evidence’, and it was in the interests of justice to try him. The Crown has to apply to the Court of Appeal to do this; the CoA will then decide whether to allow a retrial. This was the mechanism used for the Stephen Lawrence retrial, and (from memory) the Babes in the Wood retrial.
Yea, from what I remember they can now retry someone if they really want to. William Dunlop was apparently the first murderer retried that way in 2006 after being aquitted in 91 but confessing the crime afterwards.