Yes. There are very strict laws and regulations governing crematoria, which include the fact that all cremations must be separate (there are one or two exceptional circumstances where an exception can be made to this rule, which you would be made aware of at the time of arranging the funeral). Each coffin is cremated exactly as it is received at the crematorium and when the cremation is complete, the ashes are raked into a single container ready for collection or scattering. At this point, the metals are removed and recycled.