Vesta, do not panic or worry. Not wanting to take away from the stress of the phonecall from First Direct, but unfortunately you are part of the one banking group (HSBC) that do have a policy on no IVA accounts.
I have a co-op cashminder, which you can apply for over the phone (not sure why they're sending you papers, but feel free to call up straight away and apply over the phone.) You can pay cheques and cash in, in the post office, and their 24/7 UK call centres are excellent. You get internet banking and visa electron card too.
Good alternatives for IVA are Natwest and Halifax/BOS, though make sure you don't have any past debts with them.
Please don't worry though, I was with HSBC for nearly 15 years and had to walk away from them due to my impending bankruptcy, and i've got nothing but praise for the co-op, so change can be good!!
There shouldn't be any reason why you'd be turned down for one, although they may refer you to their credit department for a couple of days, but again don't panic, it happened to me and all was ok.
I also agree with Ray, that the Cashplus card
www.cashplus.co.uk is an excellent card to loan money on and use in places where a visa electron may not be accepted, or if you get the urge to flash a mastercard around - yet you're not racking up more credit!! [:D]