Depends on the local councils. Some allow, some don't. Leeds recently let taxi drivers use bus-lanes.
And immediately the private hire operators wanted in on the act too. [So far - refused.]
It's bad enough with taxi drivers allowed to use the bus lanes - and I've never understood why that is. Taxis' aren't mass transit so it just seems that if you have the money to pay for a taxi you are allowed to avoid the queues which can't be right. I also fail to see why a taxi with just the driver in is any different to any other car?
And thank goodness private hire drivers aren't allowed to use the bus lanes - congestion is bad enough on York Road due to muppet taxi drivers repeatedly tripping the bus lane priority traffic lights, without having more private hire drivers* joining in.
(Not very) interesting fact - the bus lane up York Road allows taxi's in it for nearly the full length, except the short section past Romart (where the CSH makes cyclists battle with the locals trying to get from the shop to the bus stop), which is clearly signposted 'Buses Only' and has enforcement cameras. Oh I do laugh watching taxi drivers flying up the inside of the queuing traffic and wondering why no-one will let them re-join the main carriageway at the sign...
* - some private hire drivers already do use the bus lane (including the priority traffic lights), but strangely never the section where the enforcement cameras are...