As far as I can remember this is a standard Austin-Morris steering wheel of the same era as the Bugeye and the original Mini when they first came out, ie late 1950s and early 1960s.
At this time Austin-Morris and Triumph were completely separate companies. This is not a Triumph steering wheel.
You would have seen this on the A30, A35, A40, Morris Minor, Bugeye and Minis. The only difference would be the push-in horn insert.
My 1964 Mini Traveller (died 1972) had this steering wheel, and so does my 1958 Bugeye (still going strong).
By the way I have a spare of this steering wheel in somewhat better condition than this picture suggests.