That's not what happens. If everyone is queueing properly and one car piles into the back of the queue pushing cars into one another then all claims will be dealt with by the insurer of the car that started it all. It differs if there are multiple incidents, eg in fog, where one car goes into...
If it's the other driver's fault then both claim against him. No need to claim against the cyclist for him then to recover against the driver, it doesn't work like that.
Depends on who was at fault for the accident! You only said an old man was knocked off his bike by a car. If it was the cyclists fault you would, legally, have a claim against him but if it was the driver's fault then the whole claim is against him and you don't need to pursue anything against...