You don't say whether he helps around the house, cooking, cleaning, laundry, DIY, bins etc. Nor do you say whether £100 genuinely covers 50% of your outgoings. I bet the division of cost and labour are not equal. But they should be.
Years ago I heard that to get your adult children to 'launch' (ie to become an independent adult) you need to massively decrease comfort at home. Not make it unloving or unpleasant but just don't make it easier for them than it is for you! Don't cosset them.
I'd start by doing the maths on what it costs you to keep him in this semi- hibernation state and up his expenses so he's paying his full share, including rates, council tax, home maintenance eg new white goods and boiler etc. Not to be mean, but to treat him like an adult, since he is one.
I'd do the same on hours spent on housekeeping. Split them 50/50 at all times. Apart from anything else, the cooking and cleaning will get him out of his room. Again, not to be mean, just tell him he's not a teen any more and he needs adult life skills and to share adult responsibilities, otherwise you feel you're letting him down by treating him like a big child who is incapable of running a home, when he's perfectly capable of adulthood.
Could you spark some chat with him about what a full life is. It's pretty common knowledge that happiness stems from feeling you belong, from enjoying and contributing to the world, from taking healthy risks and growing, from taking action towards dreams or goals. . Maybe both make up fun lists of three good risks you dare the other one to take - like going to a gig on your own, joining a fitness group or sports club, signing up to volunteer for some charity or political or eco group you believe in.
He may say he's tired, but ask him if he really wants to be delivering furniture and sitting in a tiny room until he dies. If not, he needs to get out in the world. Fitness training will give him energy, volunteering will give him self worth. Then he can start dating and he'll have more life experiences to talk about.