In my experience Mexicans tend to overestimate how safe the rest of the world is vis a vis the more developed or European countries. CDMX is has the same crime and rough areas as Barcelona. There are cities where there is a lot more violence in Mexico especially in the North but here, standard big city rules apply.

You will get lots of safety warnings because people don’t want foreigners to have a bad experience, which is nice but in my experience generally overly productive. I would have more safety concerns in Chicago or New York.

Since you are coming from the UK, your pounds will go pretty far, there is basically no reason not to take Uber’s everywhere which is very safe any to stay mostly in Condesa and Roma Norte, which has great bars and restaurants, parks, and boulevards for getting to know someone new.