It's not the first time a game name has been reused. The 8-bit era espectially has had a tendency to let it's copyrights lapse.
According to
WOS, there were
at least two games on the Speccy called Bedlam
strawberry float knows who, if anyone, still owns the rights to these titles today, though. (The one you're referring to is by Go!, who IIRC, were affiliated with US Gold, though another site gives the developer as Beam software who were originally part of Melbourne House.)