Is there no other way to connect me to the fibres that pass my home
TL;DR: The wrong sort of fibre.
The fibre passing your home is really a distribution fibre, which is a lot of fibres bound together, and destined for a node with splice trays where it can be jointed. Even then, each fibre would be shared by dozens or hundreds of homes, with more hardware necessary to achieve that (as either an FTTC cabinet or splitters and DPs).
BT aren't going to randomly cut into their distribution cable to splice one odd fibre for you ... just as they wouldn't do that with the main 500-1000 pair copper distribution cables either.
In electricity terms, it is like asking for a 240V connection, then wondering why you can't be connected to the 400kV national grid line that goes over your house. There's a lot more hardware needed before it is suitable for an individual home.
Is there not some "box of
tricks" that could be fitted in the fibre close to my home? Any other
technology that could utilise that 2 miles of copper wire more effectively?
Yes, there is a box of tricks: another FTTC cabinet even closer. Or some variant of FTTP would need to be fed to you (but likely from further away than the cables running outside your house).
However, either style of "box of tricks" would cost money to get to you. Who pays that?
To BT (and their BDUK funders), it is a matter of balancing the costs against the outcome. And that box 600m away will do just fine - it will supply you at speeds within the BDUK targets.
If that isn't enough for you, then the onus of funding will fall to you personally.
BT have a product line that allows you to order "FTTP on demand"; the intention is that it would be available to everyone who has FTTC available, but it is currently only available in some locations. And it is expensive.
Someone on here has ordered an FTTP-on-Demand connection as a business connection. To cover installation in the 600-800m band, he's been quoted an installation cost of £3.5k, and a monthly rate of £300pm. All plus VAT.
http://forums.thinkbroadband.com/fibre/f/4526073-bt-...