There is a Universal Service Obligation, just like in the days of voice telephony, which says the incumbent (British Telecom in most of the country) is legally obliged to offer anybody who wants it at least a minimum service (10Mbps down 1Mbps up asymmetric, so mediocre DSL basically) for a fee. In unusual cases (imagine you live on an otherwise uninhabited island for some reason or up a mountain) you may need to contribute to capital costs for installation.
About 2% of the country are estimated to /live/ in places that can't get USO obligatory service (without new construction) if they asked. Unsurprisingly people who want fast Internet don't tend to buy properties with problems like that, but in principle if you were stubborn you could buy one and demand they fix it to 10Mbps up 1Mbps down.
So, whatever it is the problem is not Connectivity.