To be honest you should consider a degree course and not HND as it won't be enough to cover things in enough detail to give you a chance at getting a job, be it in a games industry or other creative sectors.
I'm doing Computer Games Technology and we covered lots of software skills, like photo editing, graphics, 3d modelling, website making then pure art and programming and similar. Then we get to specialise in graphics or programming area. Which leads to various jobs.
It really depends what your course teaches you. Is it more art/graphics based or programming (c++/c# ? ).
If you're learning games programming, the real stuff and not silly flash scripting, then realisticaly if you get good, have code portfolios and programs to show, you can easily get a job in the games industry- obviously small indie companies but some other 'bigger' UK based ones too like Climax, Jagex games. Thery always reqruit graduates. You can even take your skills to software programming, making complex databases, websites just everything to do with the programming language you learnt. So make sure to get good with C++ then other languages will come naturaly.
If your qualification is more about 3d modelling/graphics then there are jobs in the films industry, special effects, rigging all that jazz. TV adverts, music videos even medical applications. Media based stuff is all around us really, you could be modelling the next ferarri car from someones technical drawings
you never know.
However seriously consider if HND is worth it, if it covers enough ground on the skills you need to get a job. Is it a reputable HND? How many other students went out to get jobs after finishing it? Ask the lecturers, other current students.