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That looks like a wood batten packer adjacent to your finger in the first photo.
And it's probably sodden, helping the do along nicely.
I'd say dig it out with a point object but if there's one you can see, there's others you can't.
What's happening above the frame? If that's not sealed, I'd guess it was leading to most water ingress.
NotThamesWater-
Top of the frame is an unknown, I'll investigate tomorrow but it's not as large a gap apart form the crumbling corner photographed. This is our third winter here, and although I'd noticed historic staining to the paint around the door we hadn't previously had a noticeable reoccurrence (unlike the wonderful mould doing its thing right now). Digging packers out is more effort than I can face, can I not just seal in and forget about them while they gradually either rot away or very slowly dry out over the coming years?
6pt
I’ve got some French doors around which we are seeing moisture ingress/damp. Inspection immediately reveals why. Am I right in thinking fill with some kind of expanding foam, cut back, mortar over the top? Gap is about 55mm deep, goes up to 8mm at its widest. My usual DIY approach is to pay someone to do things, please instruct me in the simplest possible terms.