your first port of call should be sainsburys to try to get a refund but you will need a receit to prove that you definatley purchased the item/s after the sell by or use by date, otherwise they will likely think you are ********ing. with a receipt you will very likely get at least a refund or replacement, then it depends if you feel you have further complaint to make for example if you beleive that the store is deliberatley selling goods which are out of date or if they are difficult about giving you your money back even with a receipt ( i really wouldn't bother if you don't have any proof).
It depends how much of a fuss you want to make really. If you take it back to sainsburys they by rights have to give you a refund and I think they have to replace the item too.
If Sainsbury's have sold out of date food, especially if it was a 'use by' date then they should be reported to Trading Standards as this is definitely an offence and possibly a health hazard. You will as previously said be better off with some kind of evidence to back up your claim.
I wouldn't bother with Trading Standards. You would not only have to prove it was out of date when you bought it, but that there was an intention to mislead, other than just an error. In most cases it would probably not even merit a visit to the store. I don't think it is actually an offence, although they should make people aware when they buy out of date goods. Many shops sell out of date goods cheaply.