Any riding hat should meet one of the safety requirements below:

PAS 015 (1998/2011) with BSI kitemark:  PAS015 is a safety standard for riding hats managed by the British Standards Institute (BSI). This standard is reviewed every two years and this is the highest safety standard for riding hats in terms of shock absorbency, penetration and retention.  Hats to the 2011 standard are preferable.  The BSI Kitemark is a quality mark indicating that hats are subjected to on-going quality control, usually by regular testing of randomly chosen batches of hats.

VG1 BSI mark: VG1 is a safety standard. The BSI Kitemark is a quality mark indicating that hats are subjected to on-going quality control, usually by regular testing of randomly chosen batches of hats.

ASTM F1163 2004a onwards with SEI mark: ASTM is an American standard similar to PAS 015 (1998), but it's testing doesn’t include mechnical strength (crushing). 

Snell E2001/E2016: Snell is an American standard and is a high performance standard that includes all aspects of ASTM and PAS 015 testing but includes testing for higher impacts to replicate a kick from a horse and landing on uneven surfaces.

AS/NZS 3838 2003 onwards: These are Australian and New Zealand standards respectively.

A previous standard, EN1384/BSEN1384, was withdrawn in 2016 so hats with this standard alone are no longer acceptable.