Taunton and Somerset NHS Foundation Trust, Yeovil District Hospital NHS Foundation Trust, Royal Bournemouth and Christchurch Hospitals NHS Foundation Trust and Poole Hospital NHS Foundation Trust.
Unison has been campaigning against the supercentres on patient safety and environmental grounds.
It involves transporting used surgical instruments to two remote surgical supercentres and then back again along congested roads.
Only two more trusts in the region, in North Devon and Dorchester, remain undecided about whether to go ahead with the scheme.
Graham Parish, Unison south west regional organiser, said: ‘I think practically the supercentre idea will collapse – the whole thing has just fallen apart.’
Unison will now ask the DH for £1m for each trust in the region to build an on-site decontamination facility.