although they think they are.
You need to ask them specifically which law gives them the right to search you and make a note of it, they've probably got it wrong.
State your objection to the search.
Do not give you're name, address or date of birth under any circumstances, that's for them to establish and prove.
Above all do not sign anything at all.
If asked the question "do you understand" reply "No I DO NOT UNDERSTAND", "I STAND UNDER NO MAN", "I DEMAND MY HUMAN RIGHT TO MY LIBERTY"
If they ask questions about you're health or mental state, demand a confidential meeting with a doctor, the doctor is under an obligation not to discuss you're health with anyone without your permission.

All this may seem like a lot of fuss but the police are trained to engage you in CONTRACTUAL ARRANGEMENTS, just like the rest of the capitalist system.
You do not have to enter into any contractual arrangement. All contractual arrangements must be entered into voluntarily to be lawful.
The police must prove REAL AND GENUINE grounds for suspicion that you have committed a criminal offense, or the search and or arrest becomes a criminal offense.