Final answer:
The false statement about labor relations in Great Britain is that unions refuse to work with employers of bad standing; they do negotiate. Also false is the claim that private sector union membership exceeds public sector; public sector unions remain relatively strong.
Step-by-step explanation:
The statement that unions have great power and refuse to work with any employer they find to be in bad standing is false concerning labor relations in Great Britain. While unions in the UK do possess influence, they tend to engage in collective bargaining and often work with employers to negotiate terms. The true scenario is that in many developed countries, including Great Britain, union coverage, which includes workers covered by union negotiations even if they are not union members themselves, can sometimes be extensive.
Meanwhile, the statement that membership in private sector unions is greater than in the public sector is also false. In fact, in many high-income economies, including the UK, public sector union membership is notably strong. The trend of declining union membership in the private sector is well documented and reflects broader shifts from manufacturing to services, increased global competition, as well as cultural variances in union acceptance.