I'm not sure we should be subsidizing £5k bikes, rather than something more practical.
For some people a £5k bike is practical. You won't get a lot of change from that if you're buying recumbent trikes or tandems with electric assist for example. Also applies to machines specialised for a particular form of cycling: cargo cycles, velomobiles etc. One Less Car applies, and even if people are only cycling for sport/leisure, that's probably worthwhile from a public health perspective.
Indeed, the cost of accessible cycles (along with the Cycle2Work scheme's £1000 de-facto limit) was one of the main barriers
[1] cited in last year's Wheels For Wellbeing survey of disabled cyclists.
At one point, you were able to purchase cycles adapted for use by a disabled person VAT-free, but the taxman clamped down on that. (It also meant that disabled people able to use an un-adapted cycle as a mobility aid had to pay the full price.)
[1] Second only to actual barriers: Unsurprisingly "Infrastructure" came top.