Hi. My name is*****'m looking at your question now and will post my answer or ask for more information here in a short while.
A Hackney taxi cab is not a car for capital allowances purposes so the £3,000 restriction which was discontinued for cars several years ago in any event doesn't apply. A Hackney taxi cab is plant and machinery and is eligibel for the Annual Investment Allowance. The capital allowances regime for cars and plant and machinery can be found here.
I hope this helps but let me know if you have any further questions.