Some of the exemption certificates in the original link are superseded or moved on the CAA website.
A key one that members of relevant associations may need is the exemption E4973 Small Unmanned Aircraft – SUA Operator Registration Requirements for Members of UK Model and Small Unmanned Aircraft Associations, which now exempts members of FPV UK, BMFA, LMA and SAA from registration until 23 February 2020. The previous exemption E4953 is withdrawn.