Well, in the city centers, bikes are a LOT faster than both cars and pedestrians.
Within cities, bikes should share the road with motorists.
Outside of cities, they should share with pedestrians.
I cycle a lot in inner London - zones 1 - 2 ish. There are a few cycle lanes, paths through parks, canal towpaths, etc, but mostly, i'm on the road. For me, that's fine; traffic is never very fast, and the next junction is never far away, so there's a mix of overtaking cars, being overtaken by cars, and each of us blocking the other for a little while where there's no room to overtake. Also, there are a lot of bus lanes, which are even better - fewer vehicles, and less likely to misbehave.
I occasionally cycle in outer London, and there, i'm glad of the network of long-distance cycle paths, sparse though it is. Speeds are higher, and drivers are more impatient.
I once cycled in Swindon, including across the White Hart roundabout. I won't be doing that again.
Not that the side roads were bad. Cars were better behaved than they are in Ireland anyway.
I recently had a ride from Bük to Csepreg which was mainly on a separate cycleway by the road. From Csepreg I was able to enter forest tracks which were very beautiful. I've also noticed quite a bit of new infrastructure in various parts of the country.
I can imagine Hungary becoming a very appealing cycling destination if they continue to develop the network.