Legally you can't sue for compensation. You can not be arrested by these people, as they have no power.
However you can be detained, otherwise they would not be able to stop true shop lifters and bouncers would not be able to stop violent people in night clubs.
However they need to be satisfied that an balance you may have committed an offence. They do not have to be absolutely sure.
You say about checking cctv, clearly they would not have time to roll back the tape, play it, consider and then identify any suspicious activity.
They only have a split second to say, hold on a second does something look off here.
Sometimes they get it right, sometimes they get it wrong, as these are people looking at cameras etc and they can make a mistake.
But the store is likely to give you a little bit of compensation, maybe £50 or so.
But are they allowed by law to stop you, yes.
I am sorry if this is not necessarily the answer you want, nor the one I want to give you, but I have a duty to be honest.
Can I clarify anything for you about this today please?