Having The Doctor on Earth working with UNIT to solve some kind of weird alien science thing, or an alien invasion, is a big part of Doctor Who lore. The 3rd Doctor spent most of his time headquartered near London, "working for" Brigadier Alistair Gordon Lethbridge-Stewart as a "Science Advisor" taking care of all kinds of crazy technology things. That included dealing with the Loch Ness Monster, who turned out to be a Silurian pet, and fending off several insane schemes concocted by The Master.
Consider a slightly different story-line. One in which alien invasions and alien technology are affecting England in the 1960's, but there's no Doctor conveniently on-hand to solve the problems, and UNIT doesn't exist. Instead the top-secret organization tasked with these problems is run within the British old boys network of various Sir So-and-so's. That's Counter-Measures, an extremely hush-hush way beyond top secret agency tasked with taking care of alien incursion issues and other crazy items of technology.
Counter-Measures contains most of the elements of Doctor Who, except for time travel and the alien from a hugely advanced civilization. If you like the UNIT stories, you'll like Counter-Measures.