"Torchwood" has always felt much more approachable to me than "Doctor Who," so if you found the original too cerebral, too goofy, or something else, you may find you like this. It still pertains to aliens and time shifts, but it's mostly focused right here on Earth. (Well, largely in and around Cardiff.)
This show is aimed at a more mature audience than its parent, which was always at least outwardly a kiddie show. The star, John Barrowman, plays a bisexual American from decades in the past who leads the Torchwood group, investigating temporal anomalies. Barrowman is actually gay, and ironically, actually Scottish, but having lived in the U.S. since he was 8, has a perfect midwestern American accent that must really sound jarring to BBC viewers.
Give it a try.