If you work for a company which wants you to be a TRI they will send you on the core course of their choice if it isn't done in house, at least that is what happened to me. The company I did mine with was called Aviation Training and Development, if they are still going I'm sure a google search will find them.
Alternatively, if you are planning to self sponser a TRI course in order to find freelance work it would make sense to talk to the training organisation running the TRI course and find out their requirements for the core course and who they would recommend if they don't run it themselves.