How far sociologists would agree that the welfare state has helped to create a culture of dependency in britain

Most of them wouldn't agree with the sentiment.

Explanation:

The welfare program created by the Britain was aimed to provide several aids or the poor people in Britain. These aids do not discourage people to work. They only cover basic necessities that most people have (such as food and shelter)

Ever since the implementation of welfare programs, the average standard of living in Britain has been gradually increasing. Along with the average employment  and life expectancy.

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