A spokesman confirmed it will not be renewing its lease on Brooklands House, Lancing, from which it loans mobility aids such as wheelchairs.
While the closure might be ‘unsettling’ for service-users, the spokesman said, it was ‘no longer cost-effective’ to run the service from this site.
These services will be available to people in West Sussex from centres in Hove and Rustington once the lease ends in late July.
Aaron Stevens, British Red Cross mobility aids hub manager for Sussex, said: “The Red Cross aims to help people in crisis both in the UK and overseas.
“To do this well we need to ensure we spend our money wisely and lease buildings that enable us to deliver our services in the most cost efficient manner whilst reaching as many people as possible.
“We have been looking at the suitability and viability of Brooklands House and have taken the decision to end the lease.
“While it has been used to provide wheelchairs and other mobility aids to people in the Lancing area, it is no longer cost effective to deliver our services from this particular site given the proximity of other Red Cross buildings.
“A regular review of our properties helps ensure that we are not expending valuable resources on buildings which are under-used, no longer suitable for local teams and the organisation, or are not in the best location for service users.
“In this way, the Red Cross can continue to provide valuable support to people in crisis, using donors’ support as efficiently as we can whilst delivering our services.
“People who need mobility aids can still borrow them from other Red Cross buildings in the area, including Hove.
“There is also a home delivery service for users who are unable to collect items from our centres.
“We realise that making changes to our buildings can be unsettling for those who have been involved with the service, so we are committed to putting in place a smooth transition process and communicating this change as sensitively as possible.
“We can’t offer enough thanks to our amazing volunteers for everything they have contributed to our mobility aids service and we look forward to continuing to provide our vital services to people in Lancing through alternative means.”
The British Red Cross offices in Worthing, which had been located on the corner of Shelley Road and Salisbury Road, closed last year.
At the time, the charity has said the sale of the building will not result in a loss of staff, as those affected have been consulted and relocated to its offices in Hove.
Find out more about the British Red Cross’ mobility aids loan service here