Poor Master's grade but demonstrably passionate about the field- do I stand a chance of getting a funded PhD place? I am graduating with a pass grade in my Master's degree from a good university in London.  I want to apply for a PhD scholarship at the University of Sheffield in non-communicable diseases. 

I did public health undergraduate degree and became interested in non-communicable diseases in low income countries as it's a neglected area overshadowed by the high rate of infectious diseases. I wrote my undergraduate thesis in this area. I also have a personal interest in this field because I lost my mum to cancer within one year of her diagnosis. My pass grade in the Master's can partially be explained due to difficulties with illness.

Do I stand a chance of gaining my desired PhD place, taking into account the medical reasons for the low grade and my proven interest in the field?
The obvious answers is: ask (University of Sheffield, not us) informally whether a (formal) application has any chances of success.

From my own experience in the UK, that answer depends (1) on which agency is funding the PhD studentship and (2) on any (additional) rules applied by the University/Department. AFAIK, research-council funded studentships in the UK require a minimum grade of 2.1 (upper second) in (any) undergraduate degree (but exceptions may be possible, I'm not sure). So if prior to said master course (where I assume you only obtained a 3) you managed that, this would be fine (I know a PhD student in a UK Physics Dept, who obtained only a 2.2 in UG Physics from Oxford, but has previously graduated with a first in architecture, which sufficied to satisfy the rule).