The proposals - which was leaked exclusively to LGC two weeks ago - include abolishing capping, establishing new council taxes and decentralising health spending by handing its control to selected London and metropolitan boroughs.
Croydon LBC chief executive David Wechsler said: 'Any proposal from the government to give local authorities more discretion is welcome.' But he added: 'One must have one's doubts. There is still a good deal of pressure on government to maintain the downward pressure on public spending.'
Rochdale MBC chief executive John Pierce described it as 'a bolt from the blue, although a welcome one'.
Wolverhampton's assistant chief executive, Andy Flockhart, said: 'This shows that the government regards us as a well-run authority, and one able to experiment with innovative ideas in spending and funding.'
Councils have long been keen to take on greater responsibility for health spending.
'We need to match local decisions to local needs,' Mr Wechsler said.
Although the response to the DoE paper is very positive, officials are cautious.
Birmingham City director of resources Roger Burton said: 'It will go a long way to redressing the balance of local democracy, and reversing some of the trends of the '70s, but at the moment it is difficult to envisage.'
Bolton MBC finance director Stephen Arnfield said: 'The council would welcome the proposals, although we would like to know exactly what it is about before we say anything definite.'
Mr Arnfield said he did not know yet what the criteria were for choosing the trust councils, but he was pleased Bolton was included.
To some councils the proposals did not come as a surprise. 'We have been looking at ways in which councils with good track records can be rewarded,' Bromley LBC chief executive Nigel Palk said.
'This is very welcome, but it is early days yet. When a white paper comes we can start getting excited about a return to local democracy.'
The most enthusiastic response came from Trafford MBC, a Conservative council which has been long opposed to capping.
Chief executive Allan Lewis said: 'I don't know who wrote these [proposals] but I could have written them for him.'
Overall, there was optimism tinged with disbelief.
'This is very welcome, but we will have to see something a lot more substantial than a leaked document,' Mr Pierce said.