Poor Master's grade but demonstrably passionate about the field- do I stand a chance of getting a funded PhD place?
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).