No. It is not illegal in the United Kingdom. It isn't even illegal to own a copy in Germany, contrary to conventional wisdom. If you are reading though, in public, you deserve every judgmental glare that you get for doing so (for any number of reasons)...
Why? Well, aside from the fact you are reading Mein Kampf in public, your question is more than just a legal one, really. Is it "bad" or "dangerous"? Well, yes, yes it is, but not in the legal sense, rather in the historical sense. You are interested in it because you are "very interested in WW2, Nazi Germany and Adolf Hitler", but Mein Kampf is one of the absolute worst sources to go to if you are trying to learn about those things. It is a poorly written work that ignored all discussion of its contents, is still just bad literature. It is literally barely readable, and that likely applies to someone who agrees with Hitler's repugnant ideas - one of the early leaders of the party, Otto Strasser, called it "A veritable chaos of banalities, schoolboy reminiscences, subjective judgements, and personal hatred" let alone for someone who sees them for the dreck that they are. It was a work dictated to stenographers, and the initial draft was considered so unreadable that it had to be almost entirely rewritten, but even then that barely made it palatable. Kershaw puts it well when he states:
Badly written and rambling as the published version of Mein Kampf was, it was a considerable improvement on what Hitler had initially produced, thanks to editorial intervention from a number of people.
As for its contents, it is a esoteric primary source document that is next to useless for someone to learn about Hitler and Nazism without a strong background in the history and the Volkisch movement of the 1920s. /u/commiespaceinvader has already touched on some of this here
So what this is all to say is, reading any primary source without good background from reading secondary literature is often a bad approach to learning about history. Mein Kampf in particular is an exceptionally bad way, not to mention a useless one. If you're interested in learning about Hitler, there is nothing that you would get from Mein Kampf that you wouldn't get from Ian Kershaw's two volume biography of Hitler, which of course spends time looking at the key parts of the book, but with the necessary critical analysis to actually understand the work and its context. There are a number of other works that do an equally important job in explaining Nazism, its rise to power, its aims and so on, all of which are massively more worth your time than the hundreds of pages of drivel you'd be slogging through for the sake of reading Main Kampf.
For what it's worth, Mein Kamf is incredibly boring and Hitler's writing is virtually unreadable. You aren't missing anything by not reading it.
But if you really want to, and don't want people to see it, why not get an e-copy? You can read it on your phone. You can probably even find it online for free.
What is so "interesting" about Hitler anyway?