The soft cream cheese sold in supermarkets (like Philadelphia) melts well.
I can't imagine that feta cheese would melt well but I've never tried it.

Thank you both. We’ve discovered that Feta is tricky to melt, but we had a vegan cream cheese in the fridge and that softened enough with a tiny bit of olive oil. Very grateful for your input 🙂.

Hi Sheila. I can say yes on the cream cheese, because that's how I make cream spinach (Philadelphia). I also use Gruyère Cheese but that can come from any number of animals so you'll have to check the label for sheep or goat Gruyere but definitely worth the effort to look for.

All the cheese sauce recipes I've used use milk. You can buy goats milk in supermarkets Tesco certainly sell it. In cheese sauce, custard etc you can't really tell the difference in flavour. (But its horrible in tea...) Tesco also sells both sheep, goats and sometimes buffalo cheeses. They all make nice cheese sauce.

Many thanks for your help, Paul and Yorks.

Sheila, I am dairy intolerant but find that non of the vegetable milks thicken much in sauces. I suggest you use less liquid and see if that helps. Alternatively, make the sauce with stock though I have never tried it. Ewe's milk cheese is readily available. I prefer Ossau Iraty which has a good flavour, grates and melts well and which most supermarkets sell.

Corn flour (Corn Starch), potato starch or all purpose flour will also thicken the sauce.

Thank you Arbuthnot and Paul for taking the time to advise me ... I appreciate it.

Paul, I've found that you need to use an awful lot of flour to thicken a veggie milk sauce.

Really? You shouldn't need too much - a tablespoon or two at most. The sauce/soup must come to a full boil for a couple minutes to activate the thickening agent. Then it will continue to thicken as it cools.