I then point out that on their shelf they had made me an offer to buy the said product at the said price and as it's not an obvious mistake (say 10p instead of £10) I would like them to honour their offer.
Andreas, that’s not the way it works in UK law. They are not offering to sell at the displayed price - your are the one offering to buy it at that price and, in cases where an error has been made, the shop keeper simply declines your offer. He can then change the price and ask you to offer to buy it again - it’s up to you whether to agree or not. In the event that a shopkeeper agreed to sell something that is priced in error, they are simply offering you goodwill - there is no legal obligation on them to do so.