Based on the reports of other people here and my experience a few mins ago, I dont think its possible to open this "Switch" account!
I was turned down as well, no explanation, despite having no loans/mortgages and 50K+ salary. PTSB worker said most applicants are turned down and that it seems to be only people who "had a previous relationship with TSB that qualify".
I had an account with them before I switched to Halifax originally but still no switch a/c for me.
They also didn't send me any info on the scoring system which they said they would. The staff seem to make it up as they go along.