This equipment is definitely full of puzzles and is definitely not a typical No.4 Mk.I (T).
Proving such a story can be very difficult and for what it is worth, I recommend that the owner write it down in as much detail as possible, including the serial numbers and the name of the uncle and if possible include old photos showing the rifle, sales receipt etc. I doubt that we would ever know the full story of this rifle. If the uncle is alive, definitely get a written statement from him.
Certainly if it was offered for sale it would be a difficult sale and most collectors would look at it as a parts source. At least the scope and bracket are original. The scope case appears to be original though the serial number label is very questionable. The No.15 Mk.I chest is also original though repainted. The rifle is the biggest problem. As Roger Paynepointed out, it looks like it started out as a legitimate No.4 Mk.I (T). Who made the changes and when? We know so little about changes made by post-WWII military and police users of these rifles.
This equipment reminds me of the 1950s-1960s cars one hears about in Cuba. Still running and perhaps looking good, but a far cry from the way they were when they left the factory.
The owner can enjoy this rifle as a family heirloom.