Although I have not done it in the NL, it is not quite as accepted as you say. They have similar rush hour restrictions to the UK. This based upon trains from Schipol to Amsterdam and Hilversum. May be better elsewhere.
I own a folder for the very odd occasions when I want to take a bike to London and cannot afford the risk of rejection of a non folder.
York to London is easy-peasy. Either East Coast Trains or Grand Central.
I always book through the Transpennine Express site, as they do bike bookings online and post for free. You do occasionally get a bit extra 'online discount' from EC for booking one of their trains on their site but generally the price is the same whoever you book through. Alternatively you can go to the station and book from an Actual Person there, if you have a convenient station.
If you're on an EC service, the East Coast staff at York station aren't bad at all. Go and ask the person in the kiosk next to WHSmiths if they can tell you which end of the train the bike space will be - they use two sorts of train, one with a big guards van at the london end and the other with a smaller one at the northern end with dangly spaces. The First Class carriages are always at the southern end (so the posh lot don't have to walk too far on arrival at London). Be a bit early, make sure the platform staff know you have a bike to load. They or the train guard unlock the van, hop on (big step!) and park the bike. I usually carry a couple of bungees to secure it. Hop back down onto the platform and get in the nearest door then walk through the train to your seat.
Make sure the stuff you'll need on the journey (like tickets!) goes with you and not the bike. I tend to remove lights etc and stick them in my bag so that they don't get dislodged when I'm lifting the bike on and off.
Grand Central are the best train company I've ever used with a bike. They take tandems. They take unbooked bikes. They use common sense. I've been allowed to stick my bike in the buffet car and doorways when this didn't inconvenience a anyone and was easier than getting to the guards van. I once had the train driver jump out of the cab to open up and help me load the bike on. They've also let me use the guards door between van and passenger carriage. And the driver on one was cheerful even when I accidentally got chain oil on his bag that was in the bike space.
If you are advance booking, check out the first class fares by the way. I've sometimes got first class advances for less than standard class. And they give you free coffee and food!