I do not think that the Tory party is leftist, or 'woke' (whatever that even means these days).
Sunak himself certainly didn't present as a dyed in the wool wokist in the lead up to his permiership:
> Whether it’s pulling down statues of historic figures, replacing the school curriculum with anti-British propaganda or rewriting the English language so we can’t even use words like ‘man’, ‘woman’ or ‘mother’ without being told we’re offending someone [... etc. etc.]
https://www.theguardian.com/politics/2022/jul/29/rishi-sunak...