Should I knock down existing extension first?

[Hayleazes]

https://photos.app.goo.gl/GxmpQUwNm8h74GG4A

 

Hey folks. After getting founds in a couple of years ago on my self build extension in Northumberland, and a lull due to other projects, I'm looking to make a start on my two story extension this summer. I can't decide whether to knock down the old extension (just after the two windows/lead flashing), or get some block/stone work up first. I'm just conscious of it taking a while and being left exposed if taken down prior. Any thoughts, ideas, or reasoning gratefully received!