After around midnight, it can be a bit dodgy, but you’ll be fine, especially as you’re 2 of you.
OP, London around the attractions is generally pretty safe, especially at that time. As in any other major city, common sense prevails. As you head away from Hyde Park, the areas get a bit sketchy. Generally speaking, the immediate area around U of C campus is safe. Hyde Park is a part of the south side of Chicago. As far as I remember, there were always a few dossers (pan-handlers) around the subways at the Marble Arch end of the park so it might be worth avoiding them. Hyde Park is perfectly safe at night, there’ll be loads of other people doing exactly the same as you.
Hyde Park is open from 5:00 am until midnight all year round. Recent post: What Union Represents Security Guards? Does Hyde Park shut at night?