Well you are a rubbish law student....
Individuals may not be required to have an SIA if covered by a list of exemptions under Section 4(4) of the Private Security Industry Act 2001. Some of which "could" apply to tesco or that particular store. Also many shops security are not actually security guards per se, but normal people who's job it is to place people under citizens arrest who are suspected of shoplifting (completely legal).
The following criteria would apply
Anyone who is in the act of committing an offence,
or whom the arrestor has reasonable grounds for suspecting to be in the act of committing an offence,
or where an offence has been committed, anyone who is guilty of that offence or whom the arrestor has reasonable grounds for suspecting to be guilty of it.
To "remain" legal the next critera must apply
It appears to the person making the arrest that it is not reasonably practicable for a constable to make the arrest instead
The arrestor has reasonable grounds for believing that the arrest is necessary to prevent one of the following:
The person causing physical injury to himself or others
The person suffering physical injury
The person causing loss of or damage to property
The person absconding before a constable can assume responsibility for him
Also keep in mind a private business reserves the right to refuse service to anyone as long as it is not in a discriminatory manner.
Firstly, what did you do when the policeman arrived? I presume you clearly showed him you didn't steal anything? If this is the case then I personally would call tesco's complaints department and take it from there.