For an arrest without a warrant to be lawful, two things must both be true. First, the officer must have reasonable grounds to suspect you are involved in, or attempting, a criminal offence. Second, the officer must have reasonable grounds to believe the arrest is necessary.
The "necessity" part is important — suspecting an offence is not enough on its own. The law sets out specific reasons that can make an arrest necessary, including: to find out your name or address; to stop you causing injury or damage; to protect a child or vulnerable person; to allow the offence to be investigated properly (for example to prevent interference with evidence or witnesses); or to stop you disappearing before the matter can be dealt with.
The officer has to consider whether there is a less intrusive option than arrest that would still achieve the objective. Arrest must be a proportionate step, not an automatic one.
When you are arrested you must be told that you are under arrest, and given the reason in plain language, even if it is obvious. You must also be cautioned.
This is a plain-English summary. For the exact rules, read the official PACE Code G.