People should only be prevented from travelling to the UK if there is strong reason to believe that they will commit a crime in the country.
In some of the comments above the assumption is, it seems, that as Britain is our country, we (i.e. Jacqui Smith) can decide on a whim who can enter and who can’t. However, with every exclusion there is another side: the British citizen who invited the would-be guest has his or her rights to invite foreigners to his/her home taken away totally arbitrarily.
More often than not, though, the exclusion has nothing to do with public safety and everything to do with government spin and propaganda.