There's no magic solution, unfortunately.
The 'gold standard' is Fibre To The Premises, which typically follows existing buried or overhead cable routes. The problem is the cost involved in FTTP, which is why most of the BT Openreach roll-out is the much cheaper Fibre To The Cabinet.
In some cases, network rearrangement allows deployment of a new cabinet with a Fibre To The Cabinet twin at a cost-effective price. Sadly, the necessary network rearrangement might not be able to bring together enough lines of a viable length to make this option worthwhile.
Fibre to the Distribution Point is being worked on by various organisations, but is not yet a deployable product. This is a halfway house between FTTC and FTTP - it takes fibre deep into the network, with the remaining short pairs of wires used instead of the cost of running fibre into each home. How useful this will be remains to be seen - the cost of the unit at the distribution point and the difficulty of providing power (even if this is backfed down the consumers' lines) might mean this is no more cost-effective that 'full' FTTP. Time will tell.
As MrSaffron says, any fibre deployment gets fibre deeper into the network, which provides a basis for further roll-out. FTTP On Demand might eventually turn into a good way for the subscriber and BT Openreach to share the costs rolling out FTTP in areas where there is already a fibre network.
The costs involved in the current FTTPoD product, which has only been rolled out in a limited number of areas, are not very attractive. The minimum installation cost to the ISP is £700 plus VAT, with further distance-related costs added. Anyone at the sort of distance from the aggregation node (and likely, therefore, the FTTC cabinet) where FTTPoD is likely to be of significant benefit is more likely to be paying rather more. At 1500-1999m from the aggregation node, the total installation cost is £4000 plus VAT - for anyone further away than that, it's 'price on application'.
Once FTTPoD is installed, the ISP commits to a 36 month subscription to the 330/30 FTTP product at full price - currently £38/month plus VAT. By the time the ISP has added their costs, even a throttled down service based on FTTPoD is likely to cost around £70/month.
The commercial solutions for those who cannot receive a cost-effective fibre service are likely to involve fixed wireless and, if fixed wireless is not feasible, satellite.
In areas of particular difficulty, self-help is always an option: B4RN are good ambassadors for JFDI FTTP (Just Farmers Doing It). The B4RN approach has lots to commend it, but would be difficult to implement without a lot of skills and effort being brought to the project by dedicated volunteers.
Unfortunately, you cannot defy physics or economic reality. There are always going to be some places that are difficult to serve in a cost-effective manner.