The power for a police officer to arrest an individual without a warrant comes from section 24 of the Police and Criminal Evidence Act 1984 which states that an officer may arrest any individual who they have reasonable grounds to suspect:

• Has committed an offence;

• Is in the process of committing an offence;

• Is about to commit an offence.

And it is necessary for that individual to be arrested. 

Reasonable grounds to suspect can come from many factors such as:

• Information received;

• Actions of an individual;

• Things witnessed by the officer;

• Things heard by an officer. 

The reasons why an arrest is necessary are defined by Code G of the Policing Codes of Practice and can be placed into the acronym IDCOPPLAN

I - Prompt and effective investigation into the offence ;

D - Prevent a Suspects Disappearance ;

C - To protect a Child or Vulnerable Adult ;

O - Prevent obstruction of the public highway;

P - Prevent Injury;

P - Protect public decency; 

L - Prevent the loss or damage to evidence or property;

A - Find out someone's address;

N - Find out someone's name. 

You are under arrest for having a blade.
You do not have to say anything. But, it may harm your defence if you do not mention when questioned something which you later rely on in court. Anything you do say, may be given in evidence.
The necessity for this arrest is to enable a prompt and through investigation and to prevent injury.
My name is John Doe [show card], collar number 1234, based at Mission Row Police Station.
I will now be searching you under Section 32 of PACE.
Do you have anything on you that may poke, stick or harm me?

You do not have to say anything. But, it may harm your defence if you do not mention when questioned something which you later rely on in court. Anything you do say, may be given in evidence.