The initiative is supported by Barclays' "digital eagles" project, to help people become more tech-savvy.
It will see some of the spaces freed up by the bank offer access to 3D printers and laser cutters, enabling businesses to produce and test prototypes without needing to import them from overseas.
The spaces will also be available for training sessions to teach people about cyber fraud as well as basic digital skills.
Other spaces will offer opportunities for entrepreneurs to work together and receive mentoring from industry experts.
The spaces, which are open to customers and non-customers, have been named "eagle labs" by Barclays.
Following successful pilots in Bournemouth and Cambridge, a third eagle lab is opening on Thursday on the site of a disused Barclays branch in Brighton, Barclays said.
Barclays also plans to open up to 20 eagle labs as part of a wider roll-out across the UK in 2016, including ones planned for Birmingham and Huddersfield.
As well as the business community, the Barclays eagle labs initiative will be available to community groups, children, students and the elderly, Barclays said.
The labs will carry a small charge for use of the machinery or hire for meeting rooms or event spaces to cover overheads, Barclays said. But under the current pilot, the labs are free to use on Fridays.