Rayburn integrated into central heating

I currently have a Rayburn cooker/boiler which heats the hot water cylinder in conjunction with an oil fired boiler if I desire (the hot water tank has two primary coils one for the rayburn and one for the oil fired boiler) This works nicely. The oil fired boiler does the central heating.
The rayburn circulation is done by gravity no pump involved. If I want to allow the rayburn to do some of the central heating (useful if the hot water cylinder has got fully hot) how could I integrate this into the central heating circuit. Ideally I would like to continue to allow the rayburn to heat the water by gravity and have a pump cut in once the hot water is hot to circulate the heat into the central heating the separate radiator circuit.
My question is how should I arrange my piping/valves from the rayburn to do this?

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