I believe a C6 in English will allow you to enter many poly
courses, i remember for poly courses the O level subjects
requirements are stated.
However, your overall O level results will be factored into
consideration if you apply for NTU in the future after you graduate
from poly.
O levels takes up 20% of weightage for NTU application:
http://admissions.ntu.edu.sg/UndergraduateAdmissions/Pages/PolyDiploma.aspx#addsr
As for O level English, if you do not have B4 and above, you
will need to sit for a simple Qualifying English test if you were
to apply to NTU:
http://www.ntu.edu.sg/Students/Undergraduate/AcademicServices/Matriculation/Pages/CriteriaforQET.aspx
As for NUS, it seems that only A levels English/GP or equivalent
can be used for exemption purpose.