Can an employer cut workers wages without there agreement?

No they can not change your wives employment contract or the others without an agreement being made.
However, what you must look at is the length of time being asked for a pay cut, as this can not be indefinite. The reasons why can include compulsory redundancies if pay cuts are not accepted and full closer and trading of a business if pay cuts are not taken. The company must also show that the directors are also getting a pay cut along with other expenditure cuts so to make it the least amount of cuts in a wage as possible

For basic rights on work you can look at www.adviceguide.org.uk
If you find your wife and coworkers are having problems in sorting the cuts out from management call ACAS and speak to someone there who can set up meetings so to make it balanced and fair and a term set out for a temporary contract for a pay cut. You can call them on 08457 474747.

You must state though all workers must come together and discuss this and aslong as a majority agree it can at least keep employment for your wife.

Workers have to agree to a pay cut, but they need to think carefully before rejecting the idea out of hand. Taking a pay cut can affect future redundancy payments, pension contributions and other in-service benefits. But rejecting a pay cut can lead to redundancy and closure of the business. Your wife and her colleagues need to get together and discuss the matter with a union rep or with someone from ACAS, so that they know their rights. A pay cut should be for a fixed period of time, so that the situation can be reassessed at a later date. Maybe they could come to an agreement where they stay on the same hourly rate of pay but agree to work less hours for a certain period.

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Where are you? If in the US and she doesn't have a contract that says otherwise, yes they can cut wages as long as the employees are still making at least minimum wage.

Cada appears to be versed in UK laws.

Granted in the US we don't have a lot of the same rights as in the UK, but if the employers business is in trouble, the employees may find that their paychecks could bounce if there is not enough money to pay them. The biggest expense employers have are salaries of employees. This employer could be close to filing bankruptcy if in trouble.

follow the other posters advice.