Following on from vs Following up on

"To follow on from something" means to happen after something, and often as the next part or stage of it (Macmillan):

• Following on from last year’s success, we’ll be offering other similar courses.
• What I’m going to say follows on from what Elizabeth was saying.

"To follow up on something" means (Merriam Webster) to do something in response to (something) : to take appropriate action about (something)

He says that the police failed to follow up on his complaints.

So, Following on from your email below would mean that you are continuing a chain of meaning or information, whereas Following up on your email below would mean that you are simply responding to that email.