Fines, apparently, can range anywhere from HUF 3,000 to HUF 100,000, depending on the seriousness of the offence.
I have to admit, I'm somewhat disappointed the cops aren't specifically targetting cyclists riding after dark without lights. This is my main complaint with Budapest riders, given that a lampless cyclist can pose a real threat to other cyclists, and given the abundance of people who seem to revel in being invisible.
That excepted, though, reckless peds and cyclists are mainly a danger to themselves. Law-breaking motorists, on the other hand, endanger everybody. And God knows the police haven't begun to sort them out. Come to think of it, with the loose reins kept on motorists, I'd be very surprised if the cops follow through with this jihad against us other road users.