Re: Films - meh
I think you are referring to Out of the Unknown on BBC2 which ran for 4 seasons, the first two in black & white. The first three seasons features a lot of adaptations of works by major sci-fi authors. The fourth moved away from sci-fi into psychological horror, partly because the producers were having difficulties finding suitable material to adapt and partially because they didn't have the budget to compete with new shows like Star Trek. Unfortunately many of the episodes (including some of the best) have been lost in the mists of time. Those that survive are available on DVD.
I think your "time travelling surgical knife" was probably Little Black Bag by C.M. Kornbluth, one of the stars of season 3. It is a "partial" survivor.