What kind of sausage could I use as a substitute for Cumberland sausage?
If you read the Wikipedia article you'll see that the main flavour is pepper, both black and white,and that the meat is coarser than in some other sausages. 

As it's for a casserole where the flavours have time to come together, I suggest you get sausages without herbs in (which should be easy enough). If possible they'd also have a coarser texture but that probably isn't on the label - you might have to choose based on what you're familiar with. Then add plenty of pepper to the sauce, early in the cooking. My recollection is that the white pepper flavour comes through, but I use black pepper quite heavily so maybe I'm used to that. 

The other spices (and herbs though they shouldn't dominate) vary. This recipe includes sage, which other sources (and I) say is wrong, but the nutmeg, mace and coriander all contribute to the classic flavour. While I haven't made it, the recipe I've linked should give some idea of the proportions of spice to meat,assuming your sausages are quite bland to start with. 

Edit: I should probably have been clearer that I mean links. Sausage patties aren't really a thing here in the UK. I've seen them twice. Once was McDonald's, the other may have been good but I can't remember.