They can do so, ideally the small charity would still be registered with HMRC, - they get an ID from them, before registering with the charity commission.
The other way is to set up a public subscription, and pass the funds through the Parish Council, allowing them to recover the VAT and be the ambulance service's nominated body to look after the unit - which many groups forget the ongoing maintenance costs of pads and batteries that need to be replaced.
As the Parish has a statutory power to provide and maintain lifesaving equipment, it would also be exempt from the free resource spending limit.