mahemick: i have beeen with nationwide since the 70s but im close to taking our custom elsewhere given their bl***dy stupid approach to their customers.
From what you have said I think the principal sticking point is the lack of regular income rather than your daughter's age. What a sh*t way for Nationwide to treat a customer though to be honest most banks are the same.
All is not lost however. Turn the tables on all banks with a basic bank account. They hate them because they are forced to issue them but make little money from them. It's the virtual absence of charges stoopid. Several banks offer accounts with either Visa Electron or Maestro/Solo debit cards. Lloyds TSB offer a Visa branded debit card except that unlike the Electron/Solo cards which work in Link ATMs, the Lloyds TSB card only works in Lloyds TSB ATMs. Up to you. As you know, but for the benefit of others, the Nationwide basic bank account does not offer a debit card. The solution is clear. Avoid Nationwide if you want a debit card with a basic bank account.
I hope this link is allowed as it is more complete than the Moneysupermarket table.
http://www.moneymadeclear.fsa.gov.uk/HTML/en/products/bank_accounts/basic_bank_accounts_popup.htm