whilst I have never taken an ebike on a train, I often take my normal hybrid pedal bike on trains. The local trains are run by East midland trains. All the local trains are Diesel Multiple Unit type with no guards van. Officially each train can take up to two bikes, first come first served.
I was on a train yesterday and I struggled because the whole luggage space was taken up by a pushchair. If the owner had folded it up, there would have been no problem. I had to stand up and hold my bike. Thankfully it was only a twenty minute trip.
There is no advance booking, but I have always managed to get on. The exception was when maintenance work was in progress, and the train was replaced by a bus.
My pet gripe is the lack of bike racks on buses. Especially as I have a bus pass.