What does it say here? http://dslchecker.bt.com/adsl/adslchecker.welcome
(i.e. is conventional internet slow because current residents bought slower package than is available, or is it just destined to be slow?)
If slow, digging a trench is still only an option if there’s somewhere to dig to. Is FTTP on demand available on my link above? If so you can dig to BT. But that gets expensive fast (prohibitively so). If there’s a local scheme (like, say b4rn in Cumbria) you could dig to that. Unlikely though.
Other options:
4g home broadband.3 and EE both offer something. Try and check coverage. You can mount antenna outside to improve things.
Satellite internet. SpaceX will come to your rescue eventually. In the meantime, it’s expensive but can actually be OK. Low latency means bad for gaming /video calling. Other uses it’s fine.
Wireless broadband. There are providers scattered all over. Their marketing is always rubbish, like they’d rather be kept a secret. I don’t know of any website that lists them. Get googling. They’ll survey coverage for free if you’re in their zone.
When this affected me, there were grants available to cover some of the cost difference between weird desperate internet and conventional internet. I don’t know if these schemes are still running.
If you are tensing up reading this, just buy a different house.