Our SOP asks us to complete all memory items for an engine fire by 1000 ft AGL. It tells us precisely that for any instrument failures, warning flags, etc (obviously) below 800 AGL you have to initiate a missed. But for a "simple" engine failure I can not find a straight answer.
Your question raises more questions. You say your Standard Operating Procedures dictate what you should do, but you are saying that you don't know what to do regarding an engine failure during an approach? I find this very hard to believe. Perhaps you meant something else.
When flying an approach, regardless of the minimums, if you have the means and are able to safely continue and land, then do so. If you have a problem which calls into question the safety of the flight, then going missed is most likely your answer.
You indicate any instrument failures, but clearly during an approach to minimums a failure of the clock on a precision approach would not constitute cause to go around. Failure of the clock during an approach in which the timing is the sole means of determining the missed approach point may be another matter entirely. If you've briefed an ILS but lose the glideslope, you're far better off going missed and rebriefing for the localizer-only procedure, but that's also subjective.
If you lose an engine during the approach and that's your only problem, then continuing the approach is appropriate. Do you not have an engine failure during approach checklist?