Do you need to have undergone some specialists training or hold a valid working at height qualification to be able to deliver in-house fall prevention training i.e. Tether belt with a lanyard attached to a suitable anchorage point to prevent a fall??

the answer to this is like many health and safety questions:
do you consider yourself to be competent to deliver this training?
whats your background?
do you know the difference of when fall restraint/fall arrest lanyrad would be required?
what is suitable anchorage point?
There is many sides to this question without knowing all the facts it is very difficult to answer.
I would say to you if something were to go wrong and the HSE became involved and asked you the question,"are you competent to carry out this training" what would your reply be?

Training and competence once again. Does attending a training course without gaining further practical experience qualify you as competent? No. And anyone one with a degree of competence who attends your training course will see right through you if you can't relate your own actual experiences in doing the task you're training them on.
Training on current legislation and best practice plus practical experience will make you not only competent but a much better and respected trainer.