What rights do I have to a record of a stop and search?
When they have searched you the police officer must write down:-

If the police stop you, but don't search you, they still have to write these details down. They will ask you for your name address and date of birth, but you do not have to give them this information if you don't want to, unless the police tell you they are reporting you for an offence. If this is the case you should give them the information, as you could be arrested if you don't tell them.

You have a right to request a written record of the search straight away.