If it meets the definition of a "hackney carriage", then for tax purposes it seems it's not a car, and if it's not a car, it would seem to be "plant and machinery" so you look to be able to claim annual investment allowance of 100% i.e. deduct the full £34k as an expense in your tax return, but nothing more in future years, and any proceeds you realise when you sell it will come back into your tax return as taxable income.
If you use the taxi for any private journeys, you have to pro-rata the capital allowance accordingly.
Look half way down the HMRC web page on capital allowances for cars:-
http://www.hmrc.gov.uk/manuals/camanual/CA23510.htm
It clearly says that hackney carriages aren't a "car" for capital allowances purposes so presumably that means the restrictions on relief for a car aren't applicable to your taxi.