URL change does not help
Part of the migration is a change to a new server.
online.tsb.co.uk -> internetbanking.tsb.co.uk
If you go to the main TSB site and follow the links you get there and It appears to be UP
If you use an old bookmarked you go to the old server which shows as still DOWN
Also the site could remember your (unmemorable) username for you via cookie but (inevitably) you need to actually type this in the first time you go to the new site.
These changes by themselves would cause lots of people problems so even If everything is working now I'm not surprised people are still seeing it as down.