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I'm with ChasnotRobert, if you're not planing on staying then getting builders involved for a complete rerender is opening up a massive can of worms and cost for nothing.
Can you get a hose pipe up there on the outside? I'd blast the obvious cracks to see you you can track the exact point of entry then you can do a proper job of patching up the render. I'd also get some lime mortar in the massive gap in the internal brick work if it turns out that's where it's coming in from.
You might feel a bit of a twat for not sorting it for the next buyer but you also might be making this a much bigger job than needed and a good patch up could last for years.
Claim on your contents insurance and they will claim off the buildings?