Taking them on on their home ground
I think the OP is rather hoping for the demise of the Left. Any suggestions that the Left is "dead" is a continuation of the Thatcher myth that there is "no such thing as society, only families and individuals".
There are two themes on this thread we need to think about. One is the political parties; mainly Labour / Conservative, with the marginalised left, and other parties as outside the main event. This is mostly about the who and the how.
The second thing we need to think about are the political opinions, the views people hold, their ideas about what they want, what they need. These people are mostly outside the political parties. Its the substance of politics, the subject matter of politics. What is to be done?
Supposing the Left went to places like Wokingham, Basingstoke, Basildon - all those sort of places where the Thatcherite right are based, the sort of bel-wether constituencies, the Right-wing strong-holds, and started to challenge the right on their home turf.
At first this might not seem like a good idea, in that the people in those areas would not accept the message. But on the other hand if the Left is correct in its criticisms of capitalism, something of that criticism will strike home. There are a lot of social problems out there, even in Basingstoke, and the misery capitalism creates will have an impact there.
Over a long period of time, the Left could keep on challenging the Right in those places, and analysing the things the right does, criticising it, showing up the weak points. On top of this, they could listen to what people say to them there, the people who begin to identify with the message, and then fine tune what is said to try to draw in more people.
I'm not saying the Left would necessarily ever get seats on the council in such places, (though we should not rule out the possibility), but in taking then on on their home territory, perhaps the centre of gravity of politics would shift Leftwards.
It would have a ripple effect outwards.....