Management Co. charge fees to sublet - is it legal?

Hi - first time here in a long time. Not a big portfolio landlord, just a pensioner with one property that I rent out now that I live in a different town.

I own a flat in a high rise in a small midlands town, that has an obnoxious management company who used to do their best to upset everyone until there was an unsuccessful bid by owners to buy the leasehold due to their unpopularity. Since then they have kept a lower profile but I have just received a letter saying they want a fee of £50 everytime I change tenants (doubling to £100 if not paid within 14 days), just for registering them, I presume.

I was wondering if this was legal and if I have to comply? I have been renting out for around 7 years and they have only recently thought this one up. I pay around £2,000 per year maintenance to them plus ground rent and noticed there was an interest fee plus £100 extra charge on the last bill, which upon enquiring and receiving the above letter, is an ignored fee from last year when I changed tenants.

It really sticks in my craw to have to submit to this and was wondering if anyone can advise me what to do.