Something that is worth bearing in mind here is that recovery of sums like this is often done through debt collectors, and whilst they can use intimidating methods such as threatening letters and phonecalls, they are actually not nearly as scary as they want you to believe that they are. DWF, however, are an actual law firm, and a large one at that. Sainsbury's seem to have decided that in your case they need to take a stand and recover the amounts they've lost due to your shoplifting. You can absolutely feel free to respond and ask them for evidence of the amounts that they have lost, including how they're calculating the security costs and what evidence they have to support the sums claimed. You are right that they can only recover what they have lost, so they need to either provide evidence of the value of goods that they haven't recovered (or couldn't subsequently sell), and other costs they've gone to that they wouldn't have had to but for your shoplifting. If they're employing security guards as a matter of course, for example, then it's difficult to see how you're responsible for those, but they may relate to something else. So do ask either way if you're unsure.
However, once they've provided that explanation/evidence, you need to be aware that it is absolutely possible, if not positively likely, that they will issue a claim against you if you don't pay. Sainsbury's aren't doing this for financial reasons. Instructing DWF has already cost them more than the amounts they've lost through your shoplifting, and they won't recover their costs if they win a small claim against you. They're doing this out of principle, and that means you really do need to be taking this seriously. So do question it, because they do need to establish and evidence that you owe these sums, but after that you need to find a way to pay, including agreeing a payment plan with them if that's what it takes. These are, ultimately, the consequences of your own actions, and you need to deal with them.