As edwin said, once you use credit card, there will always be fees involved. (How else would they pay me my cash back bonus? )
The only way I can think of is - use c2it, and also have your buyer/payer use a citibank credit card, and you can charge from the card, yet it is still a purchase (not cash advance). However, this is very specific (have to use both c2it and citibank credit cards), so it is not likely to be useful.
There are costs associated with operating credit card that simply cannot be avoided.
Yes, you can have it go straight to your bank but you would need to open a Merchant Account with your bank. You might want to check with them on what the procedure is and how much it would cost. Do specify that you are taking online orders as these are the ones which can approved without client's signature and thus would be apt for mail orders and internet orders.
barclays do offer merchant services,but if your a new company the cost might be a little more than you expected ,merchant accounts are very expensive .
go to http://www.barclays.co.uk for details
if you are looking for a low cost solution then http://www.freechariot.co.uk may be more suitable they pay you by bacs into your bank ,i think they charge 4.5%+25 pence per transaction yearly fee of £85 and a onetime setup of £75.
other options are hostcharge ,revecom,2 checkout and worldpay