It would probably take some time in the NHS, I have not worked in this setting for some years but my experience was that you did not see large amount of this type of patients, they tended to often be seen in a group setting, most would probably skew your data as they were older and not particularly active or occassionally fit and young but didn't often make it due to work committments.
Best thing may be to go to a couple of local hospital outpatient departments and ask them how many people they feel would fit the criteria you have...contact departments that you have done placements in as they will already know you.
As you probably need to get the data quickly for this type of study then try not to rely on any follow up or repeat questionnaires...your best bet would be a one off questionnaire.
I work in an environment where there are a lot of this type of injury, from 2/3 to maybe 10 a week possibly depending on what is going on. You would obviously need to catch them at a certain point in their rehabilitation to ask about proprioception exercises, which may be harder to do, relying on discharge to do it is risky as often patients self discharge.
I think unless you are working day in day out with this type of patient or have some good contacts to get the info for you you may well struggle to get upto the 50 you need. Your best bet is definitely local hospitals, where they run groups / ankle classes, thus you can target a bigger group in one go. Make sure when you write up that you note type of patient, previous activity, social stuff etc as these things will effect compliance.
Sorry for the waffle, hope it helped a bit.
Good luck