I assume by the British approach you mean shorter seasons, which I would be all for.
Don't get me wrong, the more Trek, the better as far as I am concerned.
That being said all of my favorite TV shows are either on HBO or AMC and they all have shortened seasons and have all been critically acclaimed and they all represent different genres.
I think Star Trek would be a perfect fit for that style of show. Plus fewer episodes mean larger effects budgets.