Grabham set up the petition following her own diagnosis with breast cancer in 2022 which was discovered during a routine screening.
Speaking to the clinicians who were performing her screening she learnt how common it is for people to drop out of appointments.
One of the main reasons they gave was that they could not get paid time off from work.
Speaking to HR magazine, Grabham said: “I realised that there is no legal right for paid time off from work for these lifesaving appointments and it’s very much a workplace lottery, if you get any time off, paid time off, have to use holidays or work the time back.’
“In a time where we have women between the ages of 50-70 working and finances can be a struggle, we should be doing all we can to offer support and ensure these appointments are attended.”
At the time of writing the petition had gained over 930 signatures.
Grabham said she has also managed to secure support from her local MP Jonathan Edwards.
Read more - Working with Cancer: a guidebook for HR
The petition will be granted a government response when it reaches 10,000 signatures and will be considered for debate when it reaches 100,000.
Whether legislation changes or not, though, Grabham said HR leaders and employers can make the change now.
She has therefore launched the free #JGHRPledge which allows businesses to commit to giving paid time off for routine breast screenings.
The pledge has received 72 signatures so far including Swansea City Football Club, Uplands Mobile Limited, Moxie People, West Wales Holiday Cottages and Green Willow Funerals.
Nicola Butt, Swansea City FC's HR manager, said the club was delighted to sign up.
She said: "We want to eliminate any financial barriers employees may face when exploring health checks, by providing them with paid time off to attend cancer screenings.
"We hope the signing of this pledge and development of our cancer screening policy will support and encourage employees to prioritise their health."
In 2021/2022, just 62.3% of women aged from 50 to 70 took up their invitation to a free breast cancer screening from NHS England.
Overall, 2.20 million women aged 45 and over were screened in that 12-month period.
Grabham added: “Being in HR we have a voice and can influence change.
“My journey has made me realise that businesses can do so much more to give better cancer support in the workplace. Starting with the pledge and by having a cancer policy in place, we can take simple steps to support employees and potentially save lives."
For HR leaders and employers seeking to provide support for colleagues with cancer, charity Maggie’s offers free support and resources for the workplace.