As a Yorkshire lass, I can say most assuredly yes. I make my own. They are not what you folks think of as pudding. Which is this gloopy stuff as I understand it.
The gravy is kind of a topic for debate. It's not the kind of gravy people in the US would have on, say, your definition of biscuits. But yes, sometimes it does have bits in it because some people use the juices from a Sunday roast to thicken it. And that tastes delightful, but it's not terribly good for you. There's a lot of fat in it.
We have brands like Bisto or Oxo, which are the base for a gravy, and we just add hot water. Stuff like this:
Personally I don't add much water because I like my gravy so thick you can stand a fork up in it. I think that's a northern thing. Down south the gravy is more thin and watery. I also add Hendos to my gravy to give it that extra something. It's like Worcestershire sauce but... better.
