This is a little silly in my opinion.
First of all, you don't need a degree in tech in order to get into tech. What the industry prize on are experience and skills. Even if you have a degree, you would be at the same starting point as if you didn't if you don't have a portfolio or something to showcase your work to employers.
Second, if anything, having the relevant professional IT certificate would be better than degrees to get into the industry. There aren't any specific to UX as far as I know, but for game design there are the Unreal and Unity certificates, and for programming there are the Python Institute for Python and Oracle for Java.
Third, if you have done college courses in UX or game design, they should be more than enough to get you into the industry. Even if you have to pay for the college courses yourself, you would still be better off than spending one year in university.
Fourth, if you want a degree that covers both as well as programming, why not just do a bachelor's degree in computer science? Computer science is a general IT degree, but it would pretty much cover everything in the tech field.
If you want specific master's degrees that cover programming, then it's probably prudent to pick computer science degrees that doesn't require relevant undergrad in computer science e.g.
https://www.ucl.ac.uk/prospective-students/graduate/taught-degrees/computer-science-mschttps://www.birmingham.ac.uk/postgraduate/courses/taught/computer-science/computer-science.aspxhttps://www.swansea.ac.uk/postgraduate/taught/maths-comp-sci/computer-science/msc-computer-science/https://www.bristol.ac.uk/study/postgraduate/eng/msc-computer-science-conversion/https://www.bath.ac.uk/courses/postgraduate-2023/taught-postgraduate-courses/msc-computer-science/#entry-requirementshttps://www.ncl.ac.uk/postgraduate/degrees/5055f/There are others, but the above is just from the first page of Google.
As far as I know, game design is neither mathematical enough nor does it have enough programming to do advanced computer science courses. UX definitely doesn't. So you would need to do a conversion course (assuming you get a high enough grade in the degree to do the computer science degree).
If you don't have A Level maths for a computer science degree, it would be signficiantly cheaper and quicker if you spent a gap year doing the A Level as a private candidate (if you can't change your choices now) than to do it later as a master's degree. The 6th form colleges might sent entry requirements for the A Level, but the exam boards don't i.e. you can do it privately even if you have no prior qualifications (you don't even need GCSEs).
I don't know what CC means, so you will need to clarify.
If you are specifically asking which of the 2 degrees would likely provide you with more employment opportunities, I would say UX. This is because game design is an insanely competitive industry and most of the opportunities in the UK tend to be via freelancing i.e. not much use. UX on the other hand is more likely in demand as well as fetching a higher salary.