I had a good look at the collapsing cliffs south of the beach car park at St Bees. Quite a lot of the pebbles trapped within it are angular, suggesting that they didn't travel far in rivers or the sea which tend to round them by bashing them together.So that's evidence that these stones were transported by ice. That last Ice Age was about 12000 years ago so there hasn't been time for it to form into a sedimentary rock. A lot of the pebbles are local sandstone but some have come further.