Yes you do have to pay a $500 USD supplement for the SQ 380 service from LHR to SIN on a RTW in C class. Refer to the current RTW fare rules at
http://www.airnzagent.co.nz/resource...123-1apr08.pdf
As far as what happens in the case of a downgrade, I would think that you should have recourse to a refund or MCO voucher from SQ since you paid extra for the 380 service, hopefully you won't be downgraded and won't need to find out.
mpc1