Most of the people in the world who work in software/computer science/technical fields didn't go to either of the two schools you've mentioned, and most of them are still successful and happy in their work. Prestige is subjective. Some people are impressed by a name, others are not. I have worked with great and not-so-great people from prestigious and unknown schools alike.
There are more factors you should consider when choosing where to study than just rank. What does the ranking mean anyway? Who ranked them? What were the criteria?
Here are some other criteria you might consider:
- Tuition and living costs
- Professors/expertise available to you. Specializations may be different between colleges.
- Quality of the teaching
- Opportunities for internships (some schools develop relationships with specific employers)
- Availability of scholarships/grants
- Graduation rates, job placement rates
- Alumni services (will there be any support, such as networking, for you when you're done?)
- etc. You get the idea...
If both of the schools you are considering have similar programs, either will likely provide you what you need: a quality education that prepares you well for your next step.
In the end, when it comes down to it, what matter most are the knowledge and skills you will have acquired. A Westminster quicksort works the same as a Queen Mary quicksort. :)