That left just a handful of providers in the market and premiums increased by as much as four-fold in some regions of the country.
But Zurich and Kerry London have said that significant health and safety and risk management improvements in the demolition sector meant they would now offer cover.
Zurich UK Commercial head of construction Carl Gebhard said: 'The higher-risk areas such as demolition are still tougher than most.
Some sectors and companies have made big improvements. Contractors often feel that insurers don't recognise when they have made changes.'
Zurich will provide employer's and public liability insurance through the scheme and its specialist broker Kerry London will carry out tests including management standards, risk management, financial security, trade activities and claims history.
Firms with good records will get greater ratings stability in the long term through the linking of performance to premiums.
Zurich plans to work with trade bodies to promote the facility to members and it will offer a rebate
clause - like a no claims bonus - to member companies that qualify.
NFDC national secretary Howard Button said: 'Policies in the sector are still high - they have probably come down about 20 per cent from their peak. I don't think they will come down that much more.
'But it is really heartening to know that it has been recognised that demolition is getting safer as a
lot of work has been done to tidy up the sector.'