Right to minimum wage
No, contractors as owner-managed businesses don't have a right to anything, let alone minimum wage. Same deal as a corner shopkeeper. You can only take out of the business whatever profit is left over after you deduct operational expenses. There is no one else to fund a 'minimum wage'. If you are not able to attract and retain paying customers, you are entitled to not eat and fall behind on your mortgage. Or get a 'proper job'. Or do something else that you can succeed at. Conversely, in the boom times, you are entitled to take large chunks of money out of that business. That's the inherent risk of any business venture.
The other posters are right. Because contracting is a form of running an owner-managed business, you compete in a free market. You cannot escape that fact. In some climates, you actively take advantage of that, when supply/demand is more in favour of the supplier. That would not be right now.
It is actually technically incorrect to say 'The customer has imposed a ten percent pay cut' because
1. It is not 'pay' like wages, it is the payment of a Time and Materials format invoice for services by the contracting company, the same kind as is put in by the cleaning company and the vending machine maintenance company. So a 'pay cut' cannot happen, the council have no idea what the contracting company pays its operatives, they only know their contribution is to its turnover.
2. Similarly, they cannot 'impose' as they have no power to do so. What they can - and rightly have done - is say 'as customers, we are no longer prepared to buy services for X pounds, we will shop around and go with cheaper alternative suppliers'. As other posters correctly say, welcome to free market business. The value of your offering goes down as well as up. The idea of 'pay cut' is better expressed as the contracting company volunteering, albeit reluctantly, a discount to its customer in a bid to retain custom in a tough market. This is no different to any other seller of anything, be it cars, fruit and veg, hifi or what have you. The company can always choose to NOT offer such a discount if they so choose. This would depend on how valued that customer is to them.
Eventually, your offering value falls to zero, as whatever offering you provide no longer meets any business needs. For IT contractors in particular, this equates to outdated skill sets - or just being a grumpy old beggar who is a pain to have around.