The six members include the chair of Telford Conservatives, Councillor Tammy Wood, and Telford & Wrekin Councillor for Horsehay and Lightmoor, Jayne Greenaway.
Both Councillor Wood and Councillor Greenaway have also resigned from the party.
The move means only one member of the management committee remains in place.
The Shropshire Star understands that a further three Telford Conservatives have also stepped down from the group's executive – which decides on the re-adoption of MPs ahead of a General Election.
Both Councillor Greenaway and Councillor Wood said part of their decision had been based on frustrations with the direction of the national party – and the way national leadership contests had taken place in recent months.
Councillor Wood said that she had also become disillusioned with overtly political rows, which she said do little to address the concerns of ordinary residents.
She said that she, along with Councillor Connor Furnival, who also stepped down from the management committee, were looking to set up an independent group of councillors to better represent the public.
Councillor Wood said: "At the last two council meetings the behaviour of councillors on both sides – you would think they were sat on green benches, but they can't make any difference to national issues and they are not talking about the problems of Mr Jones down the road."
Councillor Greenaway said she would not be standing for re-election, but would serve out her term as an independent.
She said she no longer felt she could back the party after the Government's decisions, adding: "I don't feel I am in a position where I want to support them."
Councillor Greenaway has represented her ward for nearly 16 years and Councillor Andrew Eade, leader of Telford & Wrekin Conservatives, paid tribute to her efforts.
He said: "The whole group is extremely sorry to see Jayne leave but fully understand her reasons for doing so.
"Jayne is a first rate and dedicated councillor who has always fought for the community she represents, and we would also like to place on record our thanks for all of the work she has done within the Conservative Group and will continue to support her in any way that we can."