Midland Bank's non-interest bearing current account moves from quarterly to monthly charging on 5 June.
The charge for an unauthorised overdraft moves from pounds 39 a quarter to pounds 17 a month - a rise of pounds 12 for those who are overdrawn for the whole quarter.
The charges for authorised overdrafts go from pounds 15 a quarter to pounds 7 a month - a 40 per cent rise for the permanently overdrawn.
But those who are only overdrawn for one or two months will pay less.
The charges on Midland's interest- paying Orchard account for unauthorised overdrafts rise from pounds 15 a quarter to pounds 7 a month on 10 May.
National Westminster Bank is the only bank moving to daily charging in some instances. For customers who are overdrawn by more than pounds 50 or go more than pounds 50 beyond agreed limits, the charge rises from pounds 36 a quarter to pounds 3.50 a day.
For an account overdrawn without agreement for the whole quarter the charges would mount up to over pounds 300. But those who get back into the black within 10 days will pay less.
The charges for agreed overdrafts move from pounds 19 a quarter, or pounds 23 a quarter on the interest-bearing account, to pounds 9 a month from 1 June.
Barclays Bank is writing to all customers with the new charging tariff, which comes into effect on 1 June.
The main change is that the charge for unauthorised overdrafts of more than pounds 200 rises from pounds 25 to pounds 30 a month. And the charge for a bounced cheque or Connect transaction rises from pounds 20 to pounds 25 per item. Fees for agreed overdrafts ( pounds 3 or pounds 10 a month) and unauthorised overdrafts between pounds 50 and pounds 200 ( pounds 15 a month) remain unchanged.