Most police powers to stop and search you need "reasonable grounds for suspicion". That means the officer must genuinely suspect they will find something specific — for example stolen goods, a weapon, drugs, or an item that could be used to commit a crime. The suspicion has to be based on facts, information, or intelligence about you in that situation.
Reasonable grounds can never be based on personal factors alone. Your race, age, appearance, the way you are dressed, or the fact that you have a previous conviction are not, on their own, reasons to search you. Generalisations or stereotypes about a group of people are also not enough.
Before searching you, the officer should take reasonable steps to find out (or confirm) what you may be carrying. A search must be a proportionate response to the suspicion — it is not a routine or random check.
There are some separate powers (for example under section 60 of the Criminal Justice and Public Order Act 1994) where an officer can search without reasonable suspicion, but only after a senior officer has authorised it for a specific area and time because of a risk of serious violence. These are the exception, not the norm.
This is a plain-English summary. For the exact rules, read the official PACE Code A.