**The Seahorse Trust** states on their [conservation](https://www.theseahorsetrust.org/conservation/) page

> In 2008 both British species of seahorse became protected as named species under the Wildlife and Countryside Act (1981). . .  
>  
> Another achievement, in 2010, was the banning of the use of flash photography when photographing seahorses.  This was banned on welfare grounds. After 41 years of experience we knew for certain that flash photography is harmful and kills seahorses.
>  
> It is now illegal to kill, take or ***disturb*** seahorses in British waters.

Presumably if you are close enough to photograph a seahorse, then you will be disturbing it (even without a flash), when you should be quietly leaving its vicinity, and that your business with them is only legal if you hold a licence to study them.

The [Wildlife and Countryside Act](https://www.legislation.gov.uk/ukpga/1981/69) uses the phrasing

> intentionally or recklessly disturbs

If you accidentally disturb one, that is not an offence, but to *continue to disturb it* (by taking a photograph) could be considered to be intentional.