Meanwhile, First Direct came out top for the eighth time in a row in the twice-yearly study by consumer group Which?, with 94% of its customers saying they would recommend the internet and telephone-based bank owned by HSBC to a friend.
Those which were found to have the happiest customers included names such as Norwich and Peterborough Building Society and internet bank Smile, a brand of the Co-operative Bank, while many high street giants languished further down the list.
The survey looked at current accounts specifically, although Bank of Ireland has also faced a furore in recent months for pushing up costs for some holders of tracker mortgages at a time when the bank rate has remained at a historic low.
It was not clear to what extent, if any, the mortgage controversy had impacted on the sentiments of current account holders. But overall, Bank of Ireland came bottom with a score of just 41%, receiving just two out of five stars for customer service, regular communication, clarity of statements and branch availability.
First Direct, which achieved an overall score of 85%, marks itself out with a service guarantee which offers customers £100 to switch accounts to it - plus another £100 if they end up being disappointed. Mark Mullen, chief executive of First Direct, said the bank hopes to welcome more new customers when industry changes to take the hassle out of account switching come into force in September.
Norwich and Peterborough Building Society achieved the distinction of being awarded Which? "recommended provider" status for the first time, coming in fifth place with a score of 71%. Ewan Edwards, N&P's head of current accounts, said the mutual is "delighted" and added: "We saw a sharp increase in the number of new customers switching to us following the scandals surrounding the big banks in summer last year."
Which? said big players Barclays, Halifax, Bank of Scotland, HSBC, Lloyds TSB, RBS and Santander should try harder as all achieved below-average scores of less than 62%.
The survey of 1,631 people carried out in May comes ahead of new rules which mean that from September, people switching current accounts will see incoming payments automatically redirected to the new account. The time it takes to fully change accounts will be cut from around 18 days to seven working days.