As a taxi (Hackney carriage) has a liscense to Ply for hire at the road side, it would be impractical for them to not have access to and across bus lanes. Mincab/private hire are not licensed to ply for hire and so have no business entering or crossing bus lanes.
The only reason they would want to is to save time and increase profits.
They knew the law when they started their business and no matter how big a company you are, you should not expect the law to "change" to suit your business plan.
Unless you are a petro-chemical or arms company of course, in which case, help yourself...murder, extort, occupy, steal...feel free, just don't use the bus lanes..that's the important thing