Well here we've got a wonderful thing called the National Health Service, so medical bills aren't a worry seeing as it's paid for by tax. BUT I'm not going to use that as an excuse though.
My problem with the whole 'it's going to put a strain on the NHS/hospitals' argument is this:
Money gets spent treating lots of other self-inflicted injuries, such as smoking, problems linked to obesity, injuries from car accidents, sports injuries. If your argument is going to be 'if you don't wear a helmet you shouldn't get free treatment' or 'you should face bigger bills for treatment' you're going to face the inevitable issue of the above- if you turn away cyclists without helmets, you could then legitimately turn away ANYONE.
Also: when should any helmet law kick in? Should someone be fined for going 10yards without their helmet? Going across the street? If the law operated like any traffic laws here, the above examples I give WOULD be fined, just as you'd be fined for using a phone whilst driving, or smoking and driving.