Have you any evidence that it would? whats the DNA figures for countries that do charge?
The 5p bag charge did change behaviours but it did not reduce people visiting the supermarket, which would be the aim of your charge, i believe? the charge has also had to go up quite a bit since then, as people went back to their old ways.
A more substantial charge, say £25 (not for a carrier bag!) might but then it would also deter the less well off from visiting the GP when they really need too.
As i said, i think it would be better to address the causes of waiting times, which, from my exp, is the failure to get med fit people out of hospital and either at home or into a care home.
In the case of GPs, its a longer term issue, a failure to train GPs, whatever the reasons, the Govt has failed to address these.