Beckie Hart, Director of the Yorkshire and the Humber Confederation of British Industry, said the Chancellor's job retention scheme needed to be extended to the end of June as well as further measures to offer businesses some "much-needed breathing space".
Mr Sunak announced on Tuesday that around 600,000 retail, hospitality and leisure sites will be able to claim a one-off grant of up to £9,000. The programme will cost the Treasury £4.6 billion and is aimed to help support the high street as new lockdown measures announced on Monday take hold.
Mr Sunak also announced a further £594 million for local authorities and devolved administrations to support businesses not eligible for the grants.
The latest payments will be based on the size of each store, pub, cafe or hotel tied into the business rates typically paid by each business. The smallest sites will be able to claim up to £4,000 and medium-sized ones £6,000.
However, he stopped short of extending the business rates holiday and cuts to VAT - two of the key demands from industry pressure groups.
Business leaders say small firms who do not have premises or those that are less than a year old have had no support from the Government and that that many businesses in the region "are really struggling now both with their mental health and financially".
Ms Hart told The Yorkshire Post that extending the job retention scheme to the end of the second quarter "would help firms to plan ahead and shape their investment intentions".
She said: “Businesses in Yorkshire and the Humber have strained every sinew to make it through the ordeal of 2020, and these early days of 2021 have offered no respite. Yet this remains a diverse region, which has much to offer as we look to rebuild and work towards net-zero.
“With the vaccine rollout now underway and accelerating, there really is a brighter future within reach. Businesses across the region will continue to support the NHS, employees and customers in the weeks ahead. It is vital they receive the support they need during this painful period to ensure livelihoods are protected and the recovery is delayed for as short a time as possible.”
June Smith, Regional Director North for Make UK, which represents engineering and manufacturing firms, said the impact of the third lockdown at a time when manufacturers are unravelling the implications of the Brexit deal for their businesses, means "manufacturers need clarity and certainty of the support that will be available to them for at least the next six months".
She said: "Members are telling me that whilst furlough support is welcome they need help to cover fixed costs such as business rates, and to continue to innovate and invest in skills in order to future proof their businesses, at a time when order books are down and for some, such as those in aerospace, the recovery of order pipelines to pre-covid levels can be two to five years."
Carolyn Frank, Development Manager North Yorkshire for Federation of Small Businesses, said many small businesses and self-employed workers were "really struggling now both with their mental health and financially, with unmanageable debt and reduced, or no income".
She added: "The small business sector counts for 60% of private sector employment and must be protected to avoid widespread economic failure. Support must be provided on an equal scale to restrictions, and a longer term plan made to protect businesses and jobs."