How to take off conservatory door
As isherwood noted in a comment, you need to remove the hinge pins. To get them out, it's likely that you'll also need to loosen the set screw.

Loosen the set screw by backing it off a turn or two. There shouldn't be any need to fully remove it, but if you do, that's not the end of the world, just put it back in enough to keep it from falling out.
Then remove the hinge pin which seems to bolt in. It occurs to me that the hinge pin may actually be a 2 part device, with a bolt up top that we can see and a separate one down below that's not as obvious. Without a 2nd set screw, it's not as likely, but it's possible. There may be a nut of some sort on the bottom that has to be held with another tool while backing off the bolt we can see.
Once you've got the door removed from the hinges, you can take a Phillips to the screws holding the hinges to the door jamb.
Note that the years of accumulated crud &amp; corrosion may require a fair bit of force to loosen these bolts. You may want to put a penetrating oil on and let it soak in for a while if you're meeting resistance. You should be good with the Allen head screws - those generally get a pretty good bite and don't strip often, but the Phillips screw heads will be very easy to strip out if you're not careful.