Your accountants are correct: an offshore account will save you UK tax money in your particular case.
All offshore bank accounts have the same tax benefits. Offshore accounts at banks near the UK, such as Jersey, Guernsey, & Isle of Man, are linked into the UK banking system and work seamlessly to allow you direct debit your rent, utlities, and other UK bills and to direct deposit your paycheque. You could also use an offshore account far away, such as the USA, but these will not allow direct debits within the UK.
Barclay's Private Banking has three branch offices in London and requires money going through the account of £100,000 per annum - but no minimum balance per month. I'm not sure what the others offer.