I believe I have resolved this issue...
What I did was:
Went to teams.microsoft.com InPrivate still get the problem. I then used the join org link in the private browser - I then went through a series of steps as if I was complete new (enter name / email etc), I ensure I selected my 'Work' profile.
I then received too emails, one to me as the admin of the org:
Hi, Paul
Paul Brugger (*****@tic.ie) has joined your TIC Teams org. You can manage their access in the members section in Mange org.*
And one to me as a member of the org:
Hi, Paul Brugger
You are now a part of the TIC Teams org. Say Hi! to your co-workers now to let them know you have joined them on Teams.
All appears good. There is only one Admin of the org (me) and no additional members (i.e. I wasn't added as a member) and I can access Team via the app.
It appears to me that although I was the Admin of the org something (locally maybe) was missing so I wasn't able to access the org. Having rejoined the org fixed this - be guessing!