My cards finally arrived today so I called to activate them, and while on the phone I voiced my concerns about the application process and service. The very nice lady that I spoke to logged my complaint, and said that she'd call me back with an update before 2pm.
After about 30 minutes, the phone rang and she basically apologised, said that they had IT problems and offered me £50 compensation which cancels out the annual fee, so I accepted it.
Hopefully they will pay out the Avios bonus without problems, then I think I'll be closing the account - Lloyds TSB make everything so difficult.