Starting to lever the ring forwards. You will have to start near the side, then gradually move the screwdriver down and round.
The spring-clip stuck on the rear edge of the ring
How the clip should engage, and how it engages if left to its own devices. Even as it should be there is far too much engagement, making removal harder than it needs to be.
The spring clip, pulled downwards and forward once you have managed to get the ring off (left image), and where it needs to be to avoid getting jammed behind the lip on the rear of the ring.
If it looks like the clip is going to jam in the ring then probably the best bet is to pull the bottom of the ruing far enough forward so that it clears the bottom of the bowl, then carefully lift the top of the ring over one of the two raised portions that are at the top of the bowl. You will probably need a broad-bladed screwdriver to do this.
I have seen a recommendation to cut a section out of the lip at the bottom of the ring, slightly out of line with the spring when the ring is finally fitted. Then fit the ring so the cut-out goes over the spring, and rotate the ring into its final position. To remove rotate the ring so that the cut-out lines up with the spring, and it should pull forward more easily. However that involves cutting the ring, and the cut edge will rust, and my rings at least show no sign of rotating when fitted. September 2020: At least, they didn't on the roadster, but they do on the V8. Still bothered about rust I checked them with a magnet to find that the ones I replaced on the roadster over 30 years ago are strongly magnetic, and so probably steel-based, whereas what I assume are the originals on the V8 are not! So cutting a notch is a possibility for the V8 ... but of course I can't get them off as the spring has wedged in the wrong place, I need to get the car out of the garage for more access, and its raining.
Probably the easiest I have had to deal with involved a bowl with the screw fitting as used on Minis etc, where a large, round-head screw goes up through a hole in the bottom of the ring into the fitting. By careful fitting and adjustment of the screw before fitting the ring you can set it such that the ring just goes over the head of the screw and holds the ring so it isn't loose. Ironically a replacement bowl for Vee came with the screw fitting, and I swapped it for the old clip which fortunately (or maybe not) was sound. You have to laugh but pal Terry had a car with plastic Wipac bowls with a moulded fitting for the Mini screw and no chance of replacing it with the MGB clip. However with careful positioning of the screw before the ring was fitted, the edge of the ring went over the domed head of the screw very easily, in both directions, and retained it firmly enough so it wasn't going to fall off! Maybe I should have left the screw fitting on mine.
The various screws. The four fixing screws go through the wing and a thick reinforcing ring around the aperture. The three clamp screws hold the glass and reflector, or sealed beam unit, in the frame. The adjuster screws have slotted heads that engage in tabs in the frame, and the threads go through plastic nuts and into 'sockets' in the rubber sealing that protrude through the wing, the sockets keep dirt and moisture from getting onto the adjuster threads from behind the wing. The two raised sections that retain the top of the ring are arrowed.
In September 1979 US legislation required headlamp adjustment to be performed without any 'dismantling', and modified ring ALU 1020 was provided with cut-outs (arrowed) for this purpose. Available from various suppliers in the UK: (Moss Europe)
They do look a little odd, after having been used to plain rings:
The MOT Manual beam pattern for dipped beam:
And main beam:
The headlamp mounting/reinforcing ring (arrowed) spot-welded to the back of the main body of the wing. The notches in the main part of the wing line up with the four fixing holes and the two adjuster holes.
Not seemingly available from the usual MGB suspects, this classic Mini mounting ring part No. 14A6693 seems to be the same. (mini spares)