As niggleynellie says, many professionals take on work outside their full time employment. I occasionally did staff training, privately when working for the la. The rule was any such work would be declared and done outside working hours, i.e. by taking annual leave. It worked well.
I'm probably a lone voice in feeling we should pay MP's more, they earn half what a GP does or much less than many professionals with similarly huge responsibilities and long hours. I'd increase the salary, provide accommodation in London rather than a 2nd home allowance. Any work outside their paid job to be declared on public sites and discouraged!