Apparently the chimney has been blocked off...

[BillyWillySilly]

I'm sure you mean slates you literally knock them in tight ie. until they break at the face, then keep going until the bits you have left are too small. Then point up as 2vc said, and point round the back too. Nothing will shift it then

Ummmm....YEAH! Unfortunately I don't have any slate apart from the blue garden variety. Was thinking of trying the local reclamation yard for "bits".

 

[23vc]

Just buy a single slate from your local builders /roofing merchant

 

[ted456]

Slow and easy wins the day. You are packing up a fragile arch not demolishing it.
You can take a tile and break it into bits small enough to mix with a 3:1 sand and cement mix and gently push that lot in with a small trowel - in essence you've used a lightweight concrete that will set firm and fit for purpose.

 

[ted456]

OP,
if you did go for 23vc's slate insertion suggestion then check any builder's skip for a bit of gash slate.

 

[BillyWillySilly]

OP,
You can take a tile and break it into bits small enough to mix with a 3:1 sand and cement mix and gently push that lot in with a small trowel - in essence you've used a lightweight concrete that will set firm and fit for purpose.

This makes perfect sense, I could see me making a right mess trying to ensure that there was cement above and below it, and I doubt I'd get much in the edges. Thanks!