My local Tesco has recently put up prominent signs stating, 'This caf� does not provide free newspapers', so it seems likely that Tesco's bosses are getting fed up of people 'abusing their hospitality' by doing exactly what you did.
Even though Tesco would have found it difficult to bring any criminal charges against you (because it's difficult to prove 'theft' if an item is not taken from the premises), you were clearly in the wrong and it's hardly surprising that Tesco staff (or, more accurately, the security staff who are under contract to Tesco) decided to take some action.
Whether the security guy's actions were appropriate are a matter of opinion. Some people might have simply 'had a quiet word' but. personally, I can't see that there's anything wrong with what he did. (Asking his colleague to ensure that the incident was on camera was both in his interest and in yours. It's what any good security staff would do, in order to ensure that neither of you can claim that any form of assault took place).
Legally, there's nothing you can do about it. Any store can bar whoever they like (unless it's, say, on the grounds of race) without providing any reason. You could try writing a polite letter (I don't recommend any other sort) to the manager to see if he'll reverse the decision of his security team but I doubt that he'll oblige.
As far as taking any action against the store, or their staff, is concerned, I don't think you've got any realistic chance of getting anywhere. It's not a criminal offence to upset or humiliate someone (except in specific circumstances which don't apply here) and it would be almost impossible (and very expensive) to bring a civil case seeking compensation for your distress.
Just write it down to experience and remember to pay for your newspapers in future.
Chris