If I wanted to put some sort of larder into the kitchen breast like this picture, would it need a lintel/RSJ/expensive works?

You’d probably need a lintel to support the brickwork above the door position but that’s not a huge job, just need enough brickwork at the sides to support it. The area of brick that it’s actually supporting is v small, so you wouldn’t need an RSJ.
I assume the chimney is unused and capped at roof level? The remaining void really should be ventilated to avoid the risk of damp through condensation.

Jeff