Thanks to both of you for your insights.
@TizerorFizz , you're right about the lintel repair being structural, and I definitely have a lot to learn! As for the soil specialist, our structural engineer has quoted £2-3K for the assessment, so I'm holding off on that until I better understand whether the purchase is actually pursuable. The property's foundations are believed to be fairly shallow, given the lack of a cellar and the property's age.
A bit more context: the neighbour's property appears to have undergone repairs in the past as I can see fixed cracks in the lintel amongst other signs. The tree in question is at the boundary line between our properties, though it sits beyond the front garden on the far side of the public pavement (if that makes sense). I've reached out to the local council's tree officers but haven’t received a response yet. While they likely won’t provide specific information about either property, I’m hoping to learn more about the process for regularly pollarding or trimming the tree, similar to what has been done for @SierraSapphire ’s property.
Regarding insurance, I’ve spoken with a mortgage broker who specialises in properties with subsidence history. We discussed how difficult it is to obtain insurance for properties with past subsidence issues. Insurers are generally unwilling to cover properties with a subsidence certificate less than two years old (99 out of 100 won't look at it), though they’re ever so slightly better with properties with 10 year old certificates (95 out of 100 won't look at it). However, with recent changes in the insurance market (eg. RSA pulling out of house insurance), it’s becoming even more challenging to secure coverage for properties with recent subsidence.
One option we considered was the sellers raising a claim and extending their insurance to transfer the coverage, but this requires careful handling of the insurers’ goodwill. Another would be to forgo subsidence coverage and get insurance that doesn’t cover it (assuming the lender allows this), then wait until the subsidence stabilises before obtaining full coverage.
We’ll have another talk with the structural engineers and also reaching out to a builder to get a clearer estimate of the potential costs of addressing the subsidence ourselves, considering the purchase price. In the meantime I've asked the estate agent/seller for info regarding subsidence and waiting for the response. Honestly, I’m anticipating that there may be a significant hurdle with the purchase (the sellers might even give up with us and just go with a cash buyer), but I feel it’s worth gathering all the necessary information before making a final decision. I’ll feel more confident about my choice either way, if I’ve fully explored all the possibilities.