No, not from FN or Browning, there's not.
I guess it is a normal logical jump, but it is not uncommon to FN or Browning-marked Hi Power pistols predating the Mk II Hi Power called "Mk I" Hi Powers. These pistols are the "classic" style Hi Power as typified by the T or C-series pistols. They have either a factory ring or spur hammer, a small, single-side thumb safety, checkered walnut stocks and usually have blue finishes. Fixed sight versions will have smallish sights. The rear is dovetailed into the slide while the front (semicicular) one is staked on. Adjustable sights will frequently have the "beer can" type rear and the serrated ramp front sight and base are silver soldered to the slide. These sights are tall compared to many others.
The fixed sight versions were sometimes called "Vigilant" models while the adjustables were sometimes referred to as the "Sport"...but neither were ever called "Mk I" by anyone.
This does not mean that no Hi Power-pattern pistol had such nomenclature. It is my understanding that there was indeed a Mk I Inglis Hi Power and it may be that the Indian Hi Power clones recently produced have such a model.
If I owned a Pre-Mk II Hi Power, I wouldn't call it a "Mk I". I'd call it a "72 C" if that's what it was or similarly, a "68 T" were that the case. My own approach has been to refer to the Pre-Mk II pistols as the "classic" style Hi Power.
Best.