No, there are no conditions attached to the scheme with regard to public access - you'll still have to follow the law on such matters, of course, but there are no extra requirements through SFIAnother one for @Janet Hughes Defra when she gets back to her keyboard.
I’ve asked this of many layers of administration, but few gave a clear answer. Public money for public good. That is currently airbrushed for organic matter in soils etc. But does membership of these schemes also mean public access to the land involved?