Tesco, like all supermarkets during the planning stage of the store, have to specify how many parking spaces they will have. With this information they can work out roughly how much each parking space will generate in revenue. The planning office also know this and they can restrict the number of parking spaces to reduce the profit the store makes and help local shops and businesses still trade reasonably well. The supermarkets also want to be seen to help the community and local shops by allowing you a couple of hours, knowing people parking there will also visit the local shops.
Now, if the supermarket really want to be arsey,and show you as an example, they will push to fine you for loss of revenue. I know the Tesco at the Ricoh Stadium value each space at £410 per day. If they are warning you, you can bet your life they know when you have parked there for the last couple of weeks, and they will use that to recoup loss of revenue, rather than just fine you for parking there. They do know what they are doing and will have checked all areas of the law prior to issuing you a warning or taking any action.
Want to bet your money on how good their lawyers are?
An example, Tesco wanted to do a buy one get one free on Nescafe, and insisted that's what the supplier accepted, which they didn't. Tesco emptied their shelved of Nescafe products and returned it to the supplier, who rapidly changed their mind.
Too big? Too much power? Maybe, but do you really think you deciding to fight them in court over parking is going to bother them?
