I don't like what little I can see of the GRP your boy has done. It looks as if he's chucked resin and maybe mat on top of the lead, which isn't going to end well. No sign of any trims, no attempt to address the back gulley, no wonder it still leaks.
Roofer has been up today and shared photos. Looks like the neighbour has never bothered to clean his side out and there is a garden growing up there !
The roofer is planning to remove the original shared cast iron gutter, clean everything out, fibreglass paint the under tray and then put in a plastic gutter end to end. He's also going to replace the neighbours roof with GRP like my side.
Noting the above it looks like it will be a good idea to have an annual cleaning of the gulley.
Got to agree with @^woody^ , especially if he really has used GRP, substrate has to be clean and bone dry, hasn't noticed before but your back 'gutter' is full of cr*p even after the 'repair'. And what cast-iron gutter, I'll be surprised if that channel between bay roof and main roof isn't lead.
Have you used this 'roofer' before or did you get him from one of the websites (Checkatrade etc)- if the latter I'd advise stopping now and getting some more quotes from real roofers before this one does any more damage
Just to confirm no work has been done yet. These are before photos from the first roofer. Still waiting for another to go round for another opinion.
His quote is to replace the current gutter (channel) with a plastic one, replace or fibreglass the trays (depending on wear) and then replace the neighbours original led roof in the same style as mine.
Good to hear you've got another quote lined up. Hard to tell from those pics but I suspect most of your problems are down to the buildup of rubbish in the gutter. Why is he going to replace the neighbours lead when neighbour has no leak? I don't think he's actually replaced your lead covering, it looks as if he's just painted over it possibly with mat and resin (massive bodge), possibly with Acrypol or similar (less of a bodge but design life of 5 years or so). You still have a leak so the lead obviously wasn't the problem.
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