Previously, only parents of children up to the age of six could request to work flexible hours, however under new rules, which came into force yesterday, parents with children up to the age of 16 can ask for more flexible hours.

It is estimated that an additional 4.5m parents will now be able to make the request.

Nigel Crook, managing director of Kent-based print finisher Buckingham Binders, said: "You need to know where your workforce is when you are a small company.

"We are already hit by extended paternity leave and illness, if we have two staff off at the same time we are affected."

He continued: "We employ 25 staff, we could have about half of them requesting flexible hours, if that were to happen I don't know what I would do.

"It is not always suitable and funding cover is costly. It is just another nail in the coffin of the small business."

However, the move was welcomed by Unite. Assistant general secretary Tony Burke said: "The increased right to flexible working will allow individuals to better manage work-life balance.

"Research shows it will allow businesses generally to operate more effectively in a changing society."

Yet Burke claimed that the legislation did not go far enough for the union.

He said: "The disappointing aspect of the legislation has been that the final say to any request by employees to work flexibly is left with the employer – who only has to give consideration to a request for flexible working and can turn it down with no right of appeal to an Employment Tribunal."

He added that where there is an unreasonable refusal to work flexibly, Unite advises members to seek the help and advice of a full-time regional officer.

When the new legislation was announced last year, the Federation of Small Businesses (FSB) warned that the announcement could create an "impossible position" for small business owners.

FSB employment chairman Alan Tyrrell said: "You can't have an extension of flexible working and at the same time clamp down on the means by which many small businesses cope with it, which is often through temporary workers.

"The current flexible working regime seems to be working, but the government should be cautious about extending it too far, which could be damaging to small businesses and, as a result, the millions of people they employ."