prescilla_g many thanks for looking into why this happens and your PD, I have now replied.
It's great to hear this has been raised internally, as mentioned in my message this is the primary reason for my post was to save others confusion in the future.
A bit more detail:
For anyone reading this in the interim period until hopefully this is updated, the initial text is generated when the delivery is booked into the courier's system however the code is not used on the DHL website for tracking.
The secondary text from DHL uses a new (to us) tracking number with a direct link with the tracking number already added, this works perfectly but this text is sent by DHL upon collection from giffgaff.
The reality is the UK mail website is not even needed and the package cannot be tracked using the order number, before or after collection from giffgaff.
Prescilla has kindly contacted the team responsible regarding the initial incorrect information being sent. Hopefully this will be updated shortly to a different message to save future confusion.