I can speak only for Lloyds TSB Commercial policy and practice, which I imagine, given the importance and FSA governance around responsible account opening, would probably apply across all the ‘high street’ banks uniformly.
All signatories to a business bank account would be routinely credit checked – searching for bankruptcy orders and suchlike, which could impact on their suitability for operating an account and potentially accessing company funds. If a company secretary does not require signing powers over the bank account and is not actively involved in the running of the business, we could rationale this away and allow them to be added to the account.
Under KYC rules we would define anyone signing on an account as a KAP (Key Account Party), thus many company secretaries, financial controllers and bookkeepers in addition to (usually, with SMEs) all directors. We would fully identify and verify the ID and address credentials of such KAPs before opening a business account and allowing it to be activated.
Finally, to answer the question posed, we would always recommend the enquirer to both of the main credit reference agencies to progress a personal credit report to help understand the reasons behind the rejection and to correct any errors discovered before re-applying for the bank account.