Pre booking a train ticket might be expensive via train booking websites such as traintours.lk (+94 777 80 77 90).
One of the things you might be able to do is to talk to the hotel at your departure destination and ask them to make a booking for you. This might be a good option if you want to make sure that you have a pre booked ticket especially if you are traveling with children or older people. But if you do this make sure to ask them to send you photos of the tickets as staff sometimes might be quite slack.
Ella to Nuwara Eliya, which is a quite popular route, might be difficult to get unless booked in advance. But it is much easier to get tickets from Badulla train station as it is the starting point of the train to Nuwara Eliya and there aren’t many people at the station. So if you cannot get tickets from Ella try to talk to station masters at Badulla and start your journey from there.
The train times at Badulla are around 5.50 AM, 11 AM and 17:50 PM (Might change, therefore please contact the station masters).
What I found is that it is quite easy to ring train stations in Sri Lanka to get information about departures and availability of tickets.
Try Badulla station master if you want to ask questions about Nuwara Eliya, Ella train station as it is most likely to be the least busy.
Colombo Fort (+94)11-2432908
Kandy (+94)81-2222271
Badulla (+94)55-2222271
Anuradhapura (+94)25-2222271
Also another option while in Sri Lanka is to dial 444 from your local Dialog mobile phone (this service might be available from other mobile service providers as well).
You can follow instructions to make a booking for your ticket via the mobile booking system.
For you to do this you need to have sufficient money in your mobile phone as the train ticket price gets deducted through your mobile phone.
Hope this help.