Apart from the reality of their platforms, their Ed Davey was literally a cabinet member in a Tory government and was knighted for this service by a Tory Prime Minister.

Well the fact that when the Tories got a majority of their own they reversed most of what he did in office should be in an indication that he's not actually one of them.

Labour and the Tories are not the same

No, they're not. But that doesn't make them good. Less bad, perhaps, but good is a stretch.

The purpose of the narrative that they are is to foster and maintain voter apathy.

Voters are apathetic because they rarely (if ever) get to vote for something, usually it's voting to stop something/somebody else.

It already is... in a way.

It is against the rules of both houses to knowingly mislead the house, and Parliament is free to punish its members up to and including imprisoning them (until dissolution, anyway).