Most people don't think Labour even belong at protests like such any more. Labour's only line of defence is to ask people to not turn the protest into something political (yes, I know) - aka "Don't point out how hypocritical we are, now, where's the photographer for the local newspaper?"
It happens a lot around my local area, people from smaller groups doing all the hard work and the main political parties taking the credit, usually by using the local press after telling the others that they shouldn't be going after brownie points with the public.