My (civil service) employer pays 20p a mile, but only for cycling in the course of work, not for commuting to my usual office.
I sometimes travel to meetings in other cities or abroad. I claim my 20p for Brompton travel between home and station, station to hotel, hotel to conference centre and so on.
Occasionally I need to go to York. I claim for cycling from home to York, and the only mild query I ever received was easily parried by me pointing out that the 20p a mile was a lot cheaper than driving and claiming car mileage plus parking costs, and the journey was actually quicker by bike.
There is an additional equipment allowance, and one for carrying passengers. I don't know whether these are applicable to cycling mileage, perhaps I should try one day...