Glenn played for and captained Canton (Youth). His rugby skills went unnoticed and soon he had joined Bridgend and represented Wales. His Bridgend career spanned 1981-1995, including the 1990 Welsh Cup Final at the National Stadium narrowly losing 10-16 to Neath.

Glenn played 10 internationals for Wales and scored 16pts and was the second black player to play for Wales. His Test debut came on Jun 12, 1986 v Tonga at Nuku A'lofa.

'Glenn was a squad member in the inaugural Rugby World Cup 1987 squad, scoring 3 tries v Tonga in a 29-16 win in Palmerston North, New Zealand (the first player to score an hat-trick at the Rugby World Cup). Glenn had already scored 2 tries when he was hit under the chin by a flying tackle from their full-back, Tali Ete'aki, and was concussed for the remainder of the match, however with two substitutions already made, there was no option to leave the field, or leave the side down to 14 men, but continue. Mazda Motors had put a car up for grabs for the best try of the tournament and when Mark Ring called the ‘Mazda’ move (a complicated move of switches and missed passes), Glenn’s instinct took over. When he received the ball, he went on a 90m run which left a string of bemused defenders in his wake, but as he swept in under the posts Mark had to scream at him to ground the ball for his third try. Sadly for Glenn, it was his last action in the World Cup as his concussion ruled him out of Wales' run to third position in the tournament. He also missed out on the Mazda - his third try against Tonga was nominated, but the prize went to John Kirwan for his score in the World Cup-opener against Italy'. (Ref. Tongan Treble eludes Webbe by Sean Davies, BBC Sport RU, Thurs 9 Nov 2006).
Highlights here:- https://www.youtube.com/watch?v=sepgzWe_7qU

Glenn's last Test came on Dec 10, 1988 v Romania at Cardiff.

"Webbe still working wonders on the wing".

"The 32-year-old Webbe's loyalty is a throw-back: he never even wanted to leave Canton, his junior club which was run from a pub in Cardiff, and he was determined to prove his international worth without leaving Bridgend. This he did 10 times, though he feels it could have been more were his temperament more suited to the gnashing of teeth when the heat is on - the rugby norm - rather than to laughing and joking. As in 1988, when he was one of four right- wingers picked for Wales: 'The selectors said there was a position for me on the left-wing. So I suggested they move Ieuan Evans across. I thought I was making a joke but it fell on deaf ears and I got dropped.' And so ended an international career worth five tries”. (Ref. The Independent, Sunday 25th September 1994).

(Further reading:- The Gloves Are Off : Glenn Webbe – Welsh Rugby's First Black Icon – by Geraint Thomas, Publisher Y Lolfa, 2019).