In England and Wales the law on arrest is covered by the Police and Criminal Evidence Act 1984.
(2) If a constable has reasonable grounds for suspecting that an offence has been committed, he may arrest without a warrant anyone whom he has reasonable grounds to suspect of being guilty of it.
(4) But the power of summary arrest conferred by subsection (1), (2) or (3) is exercisable only if the constable has reasonable grounds for believing that for any of the reasons mentioned in subsection (5) it is necessary to arrest the person in question.
(5)The reasons are
(e) to allow the prompt and effective investigation of the offence or of the conduct of the person in question;
(f) to prevent any prosecution for the offence from being hindered by the disappearance of the person in question.
Lestrade has reasonable grounds for suspecting that an offence (attempted murder) has been committed, and he also has reasonable grounds to suspect that the cameraman of being guilty of it (being related to one of the dead soldiers and being present at the wedding). Lestrade is therefore allowed to arrest the photographer to allow the offence to be investigated and to prevent the photographer from fleeing.
Whether the photographer will eventually be convicted of the attempted murders depends on the evidence found during the investigation. There's probably all sorts of forensic evidence for a start, eye-witnesses who can place him at the scene of the first attempted murder, there's also a good chance that he's one of the people who were sending death threats.