However, unions have condemned the move announced yesterday by Jo Swinson, calling it 'utter madness'.
A 90-day consultation period is needed before an employer can make 100 or more redundancies. Following yesterday's announcement, it will be cut in April 2013 to 45 days under regulations to be drafted early in the new year.
Speaking to HR magazine, Cartwright said: "Providing the consultation is still done properly, I believe the cut will prove to be extremely beneficial to both business and employee.
"I can understand the point of view from unions who may be worried it could lead to easier sackings but the worker will still have protection. And of course there may be some unscrupulous companies that may look to take advantage of the situation but that can happen in all areas of business."
Cartwright added: "I welcome this move and believe it's a helpful step in the right direction."
Trade unions have reacted angrily to the proposal. The union, Unite, insists the 90-day rule gives bosses, their workers and unions the best chance of trying to protect jobs through negotiation.
General secretary, Len McCluskey said: "This is one of the most regressive, anti-job measures ever taken by any government.
"To be taken in the depths of this financial crisis when the economy faces a triple-dip recession is utter madness.
"Scything back the consultation period for larger scale redundancies, from 90 days to 45 days, is akin to hanging a massive 'exit here' notice across Britain's businesses."
TUC, general secretary, Brendan Barber said: "The last thing we need is for the Government to make it easier to sack people.
"Unemployment has not gone as high as many feared because employers have worked with unions to save jobs, even if it has meant sharing round fewer hours and less work.
"The need to consult unions has made an important contribution to that, and also given staff, many of whom will have had years of loyal service, time to think through their options."
Barber added: "These measures will not create a single extra job. The idea that an employer will change their mind about taking someone on because the statutory redundancy consultation period has been reduced from 90 to 45 days is close to absurd."
The British Chambers of Commerce welcomed the change, which it believes will help to cut the red tape that businesses say strangles their ability to grow.
Adam Marshall, director of policy at the BBC, said: "In the 21st century, requiring a business to spend a quarter of a year consulting on how to restructure is unnecessary, frustrating and potentially disastrous.
"The new rules will encourage firms to focus on quality consultation with staff and enable timely but fair decisions. This greater flexibility to change direction more swiftly reduces uncertainty for employees and customers and may help to prevent further job losses where the survival of the business could be at risk."
Bev White, managing director of HR consulting at Penna, said: "In general, the change of policy to a shorter consultation is beneficial to employees as well as employers.
"An extended consultation does cause worry, uncertainty and business disruption at a time the economy can ill afford. A longer consultation will have a detrimental impact on productivity and take even longer for the organisation to bounce back from. Longer consultation periods will impact individuals careers at a time when people need clarity.
White added: "Good quality career conversations can focus people on a positive future."
This announcement comes a year after HR magazine launched its Crush Complexity campaign, urging Government to simplify employment law.
