I don’t have a 4k player. I but blu-rays.
I have not made the jump to 4K either. For one, my 1080P TV is still going strong. Also, I have glaucoma in one eye and my wife has macular degeneration. I doubt we'd see much of an improvement over Blu-ray (I have a ton of those). When my TV dies I will make the jump to 4K.
Kino-Lorber released both Dr Who films on Blu-ray and they are on sale at their website for $9.99 each. I've never been that into them. I doubt that 4K would make a big difference for these movies. They were fairly low-budget and were not shot in one of the large formats like Technirama or Ultra Panavision.