Welsh districts responded by rushing out their own prospectus for a single association, agreed with the Association of County Councils and the Association of District Councils.
Mike Perry, chief executive of Gwent CC and secretary of the AWC, said the assembly would now present its model to the 22 transition committees and the successor shadow authorities who would ultimately decide on membership.
Mass support for the AWC line would leave the proposed single association for England and Wales with a 10% loss in income.
Only seven of its 37 districts had signalled support for an independent Welsh body, it added.
The AWC argues that, as a nation, Wales would benefit both within the UK and Europe from an independent association operating in close federation with its Scottish, English and Northern Ireland counterparts.
It would 'mirror the growing independence of the Welsh Office and be ready for the establishment of a Welsh Assembly'.
In contrast, the CWD-endorsed model would reduce Wales to little more than a regional interest on a body where it held just 6% of the voting strength, it said.
The assembly also claimed independence would bring financial advantages.
'Welsh local government would have far greater influence over the resourcing, and perhaps location, of any organisations (for example, LGMB, LGIB) which might be established on a federal basis between the four national associations than it would over the same organisations in a single local authority association.'
The CWD counters that its own structure - the single association overarching a smaller Welsh association set up to deal with Welsh affairs - would give unitaries 'the penny and the bun'.
Secretary Geraint Price Thomas said it was vital that Welsh local government had a strong voice in Cardiff and London.
'We believe, for example, that the Welsh Office was working hard to develop a Welsh dimension to things like staff transfers under reorganisation,' he said.
'But we suspect that the Department of the Environment used its clout and eventually won the day' with its own proposals,' he said.
The CWD had also got an agreement that the association for England and Wales would pay half the costs of its Welsh office.
Under the AWC model, the two existing Welsh associations would combine to service the new unitary councils from May 1995, working to amalgamate properly by 1 October.
They currently employ 15 people between them with a combined budget of about £700,000.
Mr Perry said the amalgamation process would involve job losses.