Yep, Retro has been airing Classic Doctor Who every night at 8pm for the past few years. They loop through all available episodes of the classic series from the 1st doctor to the 7th Doctor.
As you probably know though, some of the early episodes are considered lost because at the time BBC reused the tapes. It's similar to what the US networks did with most of the soap operas until the mid-70s, they kept them archived as black and white kinescopes for as long as was required for FCC purposes, and then recorded over the originals since at the time no one thought there would be networks who would want to reair them decades later. It's also why many flashbacks to the late 60s-70s are in black and white even though they originally aired in color.
As you probably know though, some of the early episodes are considered lost because at the time BBC reused the tapes. It's similar to what the US networks did with most of the soap operas until the mid-70s, they kept them archived as black and white kinescopes for as long as was required for FCC purposes, and then recorded over the originals since at the time no one thought there would be networks who would want to reair them decades later. It's also why many flashbacks to the late 60s-70s are in black and white even though they originally aired in color.