A few countries do ask visa applicants about criminal convictions. (The USA, for example, demands that anyone who's ever been arrested - even if completely innocent - must apply for a visa and provide details of arrests and convictions). In such cases, approval for entry is granted (or denied) before the traveller departs from the UK. So, once again, there are no special procedures at arrival airports.
As Norman points out, EU law prevents the UK from making personal information (including criminal records) available to other countries unless there is 'justifiable cause'. (i.e. the UK can pass on specific information about suspected terrorists, drug smugglers and sex tourists but it can't open up the UK criminal records database to other countries). Many (possibly most) travellers simply 'forget' about their convictions because they know that the immigration authorities, at their arrival airport, have no way of knowing about them.
Chris
PS: Over a third of all British males acquire a criminal record by the age of 30. If the rubbish which someone has been telling you was true, there would be some very long arrival queues at airports ;-)