Not likely, I'm afraid. Cohen Media Group has Jamaica Inn and Criterion has Rebecca and Notorious. Both companies haven't released any 4K Blu-ray yet. Also, I don't think Jamaica Inn is commercially viable enough. And Notorious is released in January this year, so even if Criterion should go 4K...
I'm confused. According to this post from 2014, "Vertigo was scanned in 4k by Universal for the Blu-ray" already.
https://www.hometheaterforum.com/community/posts/4122836/
So, has there been another new 4K restoration since? Or Park Circus just saying that it's new for UK cinemas?