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The products that caused the problems in 07-08 were the ones that didn't have 30 year fixed rates (because borrowers couldn't pay when the initial teaser rates expired).
However, I suspect the UK government's appetite to guarantee everyone's mortgage is quite low. Probably the demand for 30 year fixed rate GBP paper is similarly low and would crowd out the government's own borrowing needs. Helps to have the global reserve currency sometimes!
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There's nothing inherently wrong with sub prime mortgages, either. It's a social net positive for people to have a secure home, even if purchased with 100% mortgages and temporarily underwater with some reasonably small amount of negative equity. It's still cheaper and more secure than renting if you're buying a place to live for 4+ years.
Sadly we didn't seem to learn the right thing from '08 — most mortgages in the US are still immediately repackaged/sold, and a lot of regulation added here was more about putting the boot on potential borrowers (higher deposit requirements, stress test), rather than the banks taking on a bit of risk, reflecting it in slightly higher rates, and not allowing bonkers housing inflation for a decade.
More recently, too, when all >90% mortgage products were removed, it'll only keep more people out of homeownership, and in insecure tenancies.
Hmm... Subprime though.