The appeals are made in the confederation's written evidence to the House of Commons' select committee for work and pensions, which is scrutinising the work of the HSE.
The evidence said the executive had an invaluable role to play in improving health and safety in the construction industry but concluded that it would struggle to perform it because of budgetary and structural constraints.
The confederation also highlighted the government's failure to respond to industry calls to tackle construction's £4.5bn black economy. It said in evidence:
"Firms working in this sector do not pay tax, flout health and safety regulations and produce substandard work."
It recommended once again that VAT on domestic repair and maintenance be lowered to 5% so that illegal traders had no competitive advantage.