You could try Stripe, but you will find that most card processors have some kind of buffer between payments being made and those payments being paid into your account - especially on high volume accounts.
I recommend Stripe, we have a blended rate of 0.6% + 10p for all credit and debit cards - our payments take 4 working days to hit our account (it's not hit and miss though, it's bang on every day and has been for two years). We do more volume than you do, but I am happy to introduce you to our account manager if it helps you get a good deal.
When doing a lot of sales in terms of revenue and number of transactions, credit card processors want some kind of buffer to protect themselves from chargebacks and disputes. Any processors that have offered us faster payment times have usually required a sizeable bond for up to two years. The exception here is PayPal, but their fees are obviously much higher - and also when we started out, we had 24 hour or 48 hour payments with WorldPay - but because our sales grew so much, they too wanted a bond if I remember correctly.