This surge in support follows the arrival of Covid-19 on our shores. A new poll - run by YouGov for the Trades Union Congress (TUC) - shows that employer attitudes towards flexible working arrangements have shifted markedly.
The pandemic has led to 49% of human resources (HR) managers saying that greater flexible working could now work for their firm. And another 21% of HR managers report that their business already enabled significant flexible working before Covid.
The findings were published as the UK Government's consultation on flexible working closed.
The TUC is calling for politicians to unlock the flexibility in every job by introducing a new duty on employers to include the possible flexible working options in all job adverts - and giving every worker the right to work flexibly.
That means every job ad would include details of the potential flexible working arrangements available in that role - whether that's flexi-time, compressed hours, part-time hours, term-time only hours, job-shares, home or remote working, or predictable shifts.
The successful candidate would then have the right to take up those flexible working arrangements from their first day on the job. So far around 2,000 members of the public - including parents, disabled people and carers - have used the union body to tell ministers why they need greater rights to flexible working.
Many have explained why having to wait until they are in a job to ask for flexible working is unworkable - and demanded that the Government requires employers to publish flexible working options in job ads.
The TUC says that, despite rising support for flexible working in business, only one in four jobs are advertised with flexible work options listed. It adds that a legal "right to request" flexible working has been in place for around 20 years, but that the current system is broken.
The union body states that, under current legislation, all employees can make a flexible working request after 26 weeks in a job.
One request can be made every 12 months and there is no right to appeal. The TUC believes that, without Government action, the growth in support of flexible working will not translate into practical changes for workers.
A recent survey found that half of working mums don't get the flexibility they request at work.
And that those who do get flexible working face discrimination and disadvantage as a result.
The union body’s general secretary Frances O'Grady said:
"During the pandemic, many people were able to work flexibly or from home for the first time.
"Staff and bosses both saw the benefits this flexibility can bring. But the current system is broken. A right to ask for flexible working is no right at all - especially when bosses can turn down requests with impunity.
"Attitudes to all types of flexible working changed significantly in the pandemic. Ministers need to take advantage of this - and make sure all workers can get the flexible working they need.
"Flexible working is how we keep mums in work and close the gender pay gap. It enables dads to spend more time with their kids. It helps disabled workers and carers stay in their jobs - and in employment.
"Ministers must change the law: all jobs must be advertised with the possible flexible options clearly stated, and all workers must have the legal right to work flexibly from their first day in a job."