Wolverhampton and Walsall are among four areas in England taking part in a trial.
People will be able to get support payments of £50 to £500, depending on their need, paid into a TSB bank account that only the claimant can access.
The amounts paid will be based on individual needs and will assist people with the cost of essentials such as travel, clothing and toiletries.
People can request the support by visiting a TSB branch. The bank said branch staff have received specialist training in supporting people experiencing domestic abuse.
The scheme has been developed in partnership with domestic abuse charities.
TSB also has a “safe spaces” initiative in place, for anyone needing support and to sit safely and securely to visit.
In partnership with Women’s Aid, TSB is launching a pilot scheme to allow domestic abuse victims to safely open and access a bank account, without standard documentation. The pilot will initially run in TSB’s Wolverhampton, Walsall, Norwich and Swindon branches in England. In Scotland, the Alloa, Dundee and Galashiels branches will pilot the scheme.
Farah Nazeer, chief executive of Women’s Aid said: “Women’s Aid welcomes the launch of TSB’s emergency flee fund, which addresses a vital need to help survivors escape abuse in this crisis period.”
Patrick Ryan, chief executive of charity Hestia, said: “As the cost-of-living crisis continues to deepen, we are seeing an increase in demand for our domestic abuse support services.”
Carol Anderson, director of TSB’s branch network, said: “Our specially-trained branch staff are ready to assist victims within their communities – and we would encourage any impacted TSB customers needing support to come and speak to us.”
The initiative comes days after it was revealed a record number of domestic abuse offences were recorded in West Midlands last year.
It followed the trend across England and Wales, which saw the number of crimes logged by police forces rise for the sixth successive year.
Anti-domestic violence charity Refuge said women and girls face an “epidemic of violence”.
Office for National Statistics figures show 66,011 domestic abuse-related crimes were recorded by West Midlands Police in the year to March – up from 55,820 the year before and the highest number since 2015-16, when comparable records began. It meant there were 22.6 domestic abuse offences per 1,000 people in the area last year.
The number of violent domestic abuse-related crimes in West Midlands also reached a record high last year, rising from 45,922 to 54,065.
Nationally, 910,000 domestic abuse offences were recorded in the year to March – 7.7 per cent more than the year before – and also a record.
Ruth Davison, CEO of Refuge, said the figures show “we are still facing an epidemic of violence against women and girls which shows no sign of stopping”.
Despite the rise in offences, the number of arrests and crimes referred to the Crown Prosecution Service has fallen across the country.
Across the 41 police forces that supplied sufficient data, the arrest rate per 100 domestic abuse-related crimes fell from 32.6 in 2020-21 to 31.3 last year.
Meanwhile, the number of referrals of domestic abuse suspects also fell, from 77,812 to 67,063.
However, the charge rate increased across the country for the first time in four years, with 73 per cent of cases considered by the CPS leading to a charge in 2021-22.
In the West Midlands, 1,464 cases led to 1,210 charges, meaning the charge rate rose from 77 per cent in 2020-21 to 83 per cent last year.