I'm a treasurer for an organisation and our bank account (a society/organisation account) doesn't have a card, just a chequebook.
It's never usually a problem (cheques are easiest anyway as the people we're paying are often other societies with a similar set up), however if we ever have to do a transfer it's a nightmare. They always offer a CHAPS payment (and charge £30). The only way around this is to set up a standing order that then has to be cancelled once the payment's gone through. It's a pain as we have more than one signatory on the account, so getting to the bank together can be awkward.
I understand we can't use the Faster Payments because our account doesn't have a card, but why can't they just do a normal BACS transfer? If anybody knows I'd be very much obliged because this is really starting to get on my nerves. They just shrug and say they can't do it.