I suspect that you might struggle to find out what the exact variety was as I suspect that M&S's suppliers simply send them whatever variety is in flower when they receive an order.
As an analogy, I found some utterly superb raspberries in Tesco and made a note of he variety and the supplier. When I went back a week later, in the hope of buying some more, Tesco had got what looked like the same raspberries on their shelves, in the same packaging, at the same price and from the same supplier. However they were a different variety and not as good. I kept checking for several weeks and, as I did so, I noticed that the variety on sale kept changing, even though they always came from the same supplier.
I expect it's much the same with M&S's daffodils. One of their main suppliers, Andrew Farming, was bought out by Produce Investments in 2015, with the deal including "the acquisition of more than 40 new commercial daffodil bulb varieties and 90 smaller seedling varieties".
https://www.thegrocer.co.uk/mergers-and-acquisitions/produce-investments-buys-daffodil-grower-andrew-farming/529535.article
So the daffodils that your neighbour purchased could have been from any one of a very large number of varieties. If he'd gone into the store either a week earlier or a week later, M&S might well have had a completely different variety on sale.
As has already been suggested, all that you can do is look through bulb catalogues to try to find something similar. However you need to remember that not all varieties available to commercial growers are available to grow at home.