Thanks for the additional information and for viewing the videos.
I'm not sure if Purdy is a female or male, but I'll assume a "she".
If her behavior is quite similar to the first video, then she may be experiencing what's known as a Reverse Sneeze (even though it sounds like he's snorting).
A reverse sneeze is the body's attempt to clear irritants from the back part of the nasal cavity.
Any nasal, pharyngeal, or sinus irritation can result in a reverse sneeze.
When a dog only occasionally reverse sneezes, then I don't worry about it too much but when the condition becomes chronic or lasts longer than just one or two episodes, then the following are possible explanations:
1. Nasal mites although they may be difficult to find.
Treatment is fairly easy, though, with Ivermectin given every week for three doses.
2. Foreign bodies such as a blade of grass or foxtail. Often sedation with rhinoscopy is needed to detect such a problem.
3. Allergies or rhinitis/sinusitis which may be more challenging to diagnose without additional testing but response to medication (see below) can often help to rule them in or out.
4. Polyps or masses which are best diagnosed with an MRI and possible rhinoscopy and resultant biopsy.
5. Unknown which means that we can't find an underlying reason.
6. Lower airway diseases can result in secretions that are coughed up; these may irritate the nasopharynx resulting in a reverse sneeze.
I'm not sure why I have a good explanation as to why Purdy only snorts when she's active as opposed to resting though except to saw that the area may be more irritated when she's not resting.
If this were my case, I'd suggest an over the counter antihistamine such as Diphenhydramine (which may be difficult to find in the UK) at a dose of 1 mg/lb twice a day or chlorphenamine maleate (Piriton) at a dose of 2-4 mg twice a day.
Sedation is a common side effect with these kinds of drugs.
I hope this helps and provides possible explanations for this behavior. Deb