Aha!!! My Asda ones are elsanta and not so good!
Elsanta is a very popular variety with growers and retailers, as it gives a very good crop, is very reliable, and has a long shelf life. And there is nothing wrong with it, as far as it goes. But there are much nicer-tasting varieties available.
Pick Your Own farms don't have to worry about whether the strawberries are easy to pick, or whether they have a long shelf-life - that's your problem, and presumably you aren't going to worry too much if some of them get squashed on the way home! So they can grow the less robust varieties and that's why they always taste nicer.
I have been told that one of the best kinds to get is called Marie Dubois, but I have never seen it - if you do, let me know!