No. My Tower Hamlets bill appeared on my statement this month without any problem.
I paid a surcharge of about 1.5% for card payment but on the premium BMI card (2 miles per £1, with a mile worth about 1.5p) I figure it was worth it.
These 'cash substitute' charges are getting a bit weasily - I read last week that one card issuer will now treat gift voucher purchases as a cash advance, with the 2% fee and instant interest accrual!