There is no negative to doing a joint degree in these subjects; they complement each other well, and as noted there are a lot of programmers around (who have or have not done a degree) and not so many actual computer scientists who have as strong a grasp on the abstract foundations of CS. Both are necessary to an extent, but the latter skill set is rarer (and does not necessarily preclude the former skill set).
You could also do e.g. CS with Maths Part I at Cambridge, continuing on in CS; you would get a better mathematical foundation than the average CS graduate but still have an extensive background in both practical and theoretical computer science from the main CS course. Similarly Durham's Nat Sci course is relatively flexible (and has options for both maths and CS, as well as others) so you can vary the focus between the two or switch to a single honours.
Warwick has a Discrete Mathematics degree which is ostensibly a maths degree but focused on the relevant areas to theoretical computer science and decision sciences. They also have a new Data Science course, which is more statistically oriented but has a strong computing component, and is quite relevant for both tech and finance roles. UCL also has a somewhat similar in some respects course to the Discrete Mathematics one in it's Mathematical Computation degree; this is more of a CS degree with a significant component of higher mathematics (specifically the abstract algebra courses from the single honours maths degree).
The "top" universities, or "elite" universities in this area would generally be Oxbridge, Imperial, Warwick, and Edinburgh and Durham lagging a little behind those. Sheffield is also a good option, particularly on the engineering/computing side. You may also wish to consider Southampton, which has an excellent CS department and very good maths department, which I believe has a Maths with CS course, and also has a Mathematical Studies degree which is a more flexible version of the single honours maths degree, having fewer required courses and more scope to take modules outside of the main discipline (in your case likely mathematics).
Birmingham, Bristol, and Bath are all excellent in for these areas as well. Some relevant courses you may wish to look into are Engineering Mathematics at Bristol, or if enjoy physics as well as maths and are interested in computing, the Applied Mathematics and Theoretical Physics course at Birmingham which has an option to "intercalate" a year on the Computer Science degree (although this extends the length of the course by a year).
However if your interest is in the technology sector, and you don't have an enduring love of fundamental mathematics you may find yourself burning out a bit during a mathematics course; it's a lot to take in, and pretty hardcore stuff. If you enjoy more mathematical and quantitative techniques but your primary interest is in technology and computing, I would suggest looking at CS courses, and seeing if they have scope to take additional mathematics modules as options for example.