As someone who is currently on an MSc course with significant overlap with that of MSc Flight Dynamics at Cranfield (and getting pretty desperate for that first job), let me be the first to advise you to have a backup discipline/specialisation to fall back on.
To my knowledge, there is no aircraft company in the UK apart from Augusta Westland that do significant amounts of civil flight testing (and they only do helicopters).
Of the military manufacturers, BAe Systems run a generic Aeronautical Graduate Scheme where I think the placements are rotational over the period of the graduate scheme. After the scheme ends you may/may not be placed in a function related to flight test engineering.
Qinetiq have had a long history of flight testing, but to my knowledge the organisation has dialled down its flight test activities over the past couple of decades (others here are undoubtedly in a better position to confirm/strongly deny this). I have seen an advertisement for a graduate flight test engineer on their website, but only once, and I think they normally recruit graduates onto the graduate scheme, much like BAe.
Another company worth mentioning is Marshall Aerospace, who sometimes take on graduates with flight physics/flight dynamics experience.
Overall, the number of graduates that go straight into a specialised flight test role is close to 0. Of those who do eventually go into flight test, it can often be a case of luck and a position in that department opening up at the right time. We are talking of very small numbers.
My advice to you is to finish off your undergraduate to MEng level, and concentrate on applying for a graduate aerospace scheme/job. You will find today that ANY graduate role with one of the big aerospace companies is an almost momentous achievement in its own right. For each graduate job there are hundreds of applicants.
Flight physics and flight dynamics (which forms a large part of flight test) in my opinion aren't disciplines which are particularly in demand. (At the moment structural and stress engineers are required especially, as well as manufacturing engineers. And the salaries are pretty good too.)
In my opinion don't bother doing these specialised MSc programmes in Flight Dynamics/Flight Testing until you have worked for several years in an aerospace company. As a fresh graduate they will be expensive and not particularly transferable to other jobs should you become desperate for work.
Sorry to sound pessimistic, I only want you to be aware of the reality out there in the job market. I have spent all year applying to jobs thinking that a prestigious MSc course from a prestigious university (for aerospace that is!) will open doors for me, when in fact relevant work experience and (especially in the case of flight test) luck are probably more important.