There's a bit of conflation of various items going on here: UK (and EU) and US copyright law, and the difference between essays you've submitted as a student and blog posts you've made and they've crawled.

The court case dealt with essays submitted as a student and US copyright law (which also applies to the DMCA copyright act). For student essays, the students agreed to the terms and conditions of the website, which allows Turnitin to archive the essay. The court found that the alternative is to not agree to the T&Cs, and come to a different arrangement with the school or teacher that requests it. Furthermore, it found that Turnitin's use of the work, while commercial, was sufficiently transformative as it was used for preventing plagiarism, and thus (together with the three other factors) satisfied the criteria for fair use in the US. I think the fair use argument could reasonably apply to your blog posts made, and crawled, before you signed the T&Cs of Turnitin (assuming you did as part of your course). Their legal department's approach of agreeing to take them down, then saying it was impossible because they were introduced before 2015 is strange.

UK (and EU) law is much more restrictive when it comes to fair use. As you've mentioned, there's no transformation exception. I think you're in the right there: you've informed them that all works from your blog infringe your copyright, giving examples of specific pages. They should "act expeditiously" to remove the infringing pages, but are not.