They are exempt - but some drivers will start to carry them around in the boot. A good idea is to take yours with you if you can it may be a little inconvenient but surely worth it as I've seen the way some minicabs drivers drive !! Arrggh!
I know they are large and cumbersome - so maybe a cheap holdall that it would fit in is worth the cost. If you have more than one the more inconvenient it becomes but still arguably worth it. Our local firm will ensure that the car that took you will pick you up for your return - so you might be able to leave it with the driver in his boot. A bit of a risk - but something you can talk to your minicab firm about.