I've been in that situation myself; here's what I found helpful.
First, realise that your cat's behaviour doesn't mean that he doesn't trust you. Clearly he does love and trust you; he shows that by wanting to be in your lap. So when he hides from you when you're standing up and walking around, think of it as an involuntary reflex that has nothing to do with his feelings for you.
Next, try to break the association between your action (standing up and walking around) and his response (hiding). One way to do this is to keep treats handy, and toss one on the floor when you're standing still. Gradually he will learn that good things happen when a human is standing still. Then move on to walking very slowly around the room and tossing treats. Eventually you should be able to walk normally. But make the training process gradual, and if at any point he goes back to hiding, go back to the previous stage for a while.
Another way to break the association is, next time he's on your lap, make a small movement as if you're going to stand up, but stay seated. The goal is to move just enough so that he's alert, but not enough so that he runs off. Over time, make the movement bigger. Eventually you should be able to stand up, and all he does is move off your lap and onto another part of the sofa.
If you don't already have a cat tree, I recommend you get one. It will encourage your cat to spend time high up, which is associated with feelings of confidence, rather than slinking about under things. A nice high one with a shelf where he can be at shoulder level would be ideal. This will allow him to feel less threatened when you're walking around the room. You can try approaching him when he's on the shelf, and offer him a treat or praise.