Hi,
I'm not all that familiar with Heralds, but might have some ideas based upon common Triumph construction techniques or just 1950/60s auto assembly methods in general.
I can think of three or four possibilities that I'd check:
1. Does the door sit outward (at the bottom) when compared to the front fender, the same as the rear? If so, it's most likely a matter of adjusting the lower hinge inward.
2. If not, i.e. it only appears to be out at the rear, compared to the rear fender but is okay at the front, one of two things is happening. Either the front fender is off (and the door is off as well because it's aligned to the front fender) or the door itself is twisted.
If the front fender is out near the bottom edge, and the door along with it, the fix would simply be to move both inward.
3. A twisted door might be a sign that it's been hit and repaired, or that it was reskinned and welded back together afterward without first aligning it properly (or was welded too quickly and warped due to heat). You might find other signs of either of these things: internal signs of damage or dent repair if it was hit (after removing the trim panel), or seam and/or plug welds instead of factory-looking tack welds around the perimeter, if it was reskinned. Could be a combination of these, or even a partial reskin, too.
A warped door, for whatever reason, will usually be hard to fix without removing tack and perimeter welds around the edge flange, at least. However, it's worth a shot before going to that trouble. Try putting a wood block in the door jamb near the top of the b-post, and push inwards on the base of the door. A little hard to tell from the pics, but if that's a convertible it would be a good idea to have someone on the inside bracing against the top of the b-post.
4. Which brings up another possible reason for this sort of misalignment if the car is a convertible... the b-post itself. Does it appear to lean outward at the top, especially when compared with the other (presumably well-alligned) side? If so, check the base of the b-post for any rust at the base in particular, from inside the wheel well and even from the interior (might need to peel off some glued on vinyl trim). If weakened by rust, the b-post might be leaning outward, causing the door alignment problem. Even if not rusted, the b-post might be bent outward.
You might be able to stretch some strings tightly front-to-back alongside the car, one on either side, perhaps run a string centerline too, and use a tape measure to see if anything measures off. Compare measurements side-to-side. Use reference points on the car and measure front-to-back, as well. Diagonal measurements might tell you if the car is out of square on the frame. (It occurs to me that alternatively, two or three laser levels might be used instead of string).
If you decide the b-post might be the problem, you could try parking the car parallel to a wall, about 3 feet out. Then put your back against the wall, your feet on the fender near the top of the b-post and give it a bit of a shove. Have someone else watch closely as you do this and go slowly at first and be careful not to cause a local dent on the fender or to scuff up the paint (stocking feet sometimes work best). It's hard to say how much it will move, but some movement is usually possible.
If you are nervous about trying any of the above yourself, have a good body shop look at it, preferably one that's knowledgeable about old car construction. They might be able to fix it quickly and easily, at relatively little cost.
Hope this helps.
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