Need to do a thin (10-15mm) lime render on my fireplace prior to installing a log burner and
am confused as to the types of lime available.

Hydrated, hydraulic, lime putty ?????

What are the differences and what's best to use ? It's a 1940's house and the render is to be
applied to bare (hard) bricks.

I used ordinary sand and cement to render mine when I fitted the wood burner 5 years ago and it's been fine. You can put hydrated lime in the top coat to something like 6 sand to 1 lime and 1 cement to help plasticise the mix.

get white cement ,and hydrated lime (burnt lime) we have used it without sand , or used limestone instead of sand to keep it white, we have done 1 cement 1 limestone 1 lime , for thin layers , or even not botherd with limestone and gone 1cement 4 lime , just have a bit of a experiment with diferent mixes it will all set ok , if you can get hold of a dolly blue from an old fashioned hardware store that will make it really white ,