Sharing is caring: should cyclists be allowed on pavements?

Fairly locally to us in Brighton a lady is campaigning to stop cyclists from being on the pavement. She reports that she's been verbally abused by cyclists who are intent on getting through regardless of any pedestrians also using the pavement.

Obviously, as in so many situations that involve anti-social behaviour, this is (hopefully!) a minority of people/cyclists.

It is illegal to cycle on the pavement unless it is a path designated for shared use. However, nowadays - with much busier roads and larger vehicles - it can be daunting for less confident cyclists (and/or children) to cycle on certain roads. Clearly less confident cyclists are unlikely to be the aggressive type that the campaigner is referring to, so should they be penalised because of the minority? 

And what about those pedestrians who either wilfully or ignorantly stroll along cycle lanes?

We're not condoning illegal behaviour, of course, but should careful, considerate and appropriate cycling on pavements be allowed? Surely abuse is unacceptable in any situation, regardless of the context? 

What do you think? Should the law be updated? It (along with lots of 'lesser' crimes) doesn't seem to be enforced as a rule so is it worth having at all? We're discussing this (and other topical issues!) on our Facebook page.