On what evidence could the police arrest MayFly man?

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.

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(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

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(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.

They can arrest him because there is a reasonable chance he is responsible for two attempted murders, has made statements which suggest his guilt, has made no denial, has been accused by a reliable witness, and the victim is in danger of a further attack.

None of these should be sufficient to convict, but they are sufficient to arrest.

There is actually strong evidence to get Jonathan Small convicted.

1. He is related to a person who died under Major Sholto (Revenge a major motive)
2. He is present in both the crime scenes taking pictures with both Sholto and Bainbridge prior and there are witnesses who could identify him.
3. How he was dating all the women with his false identities and using the places where people had just died as a meeting spot, using all these false identities is no serious issue but if you look at the first two points it would add a cynical nature behind these actions.
4. He mentioned to Sherlock and Lestrade that Sholto wasn't a good guy at the end which pretty much serves to the point that he was wiling to take up the punishment for the attempted crimes he committed.

Plus also Sherlock also mentions that he gave himself away by returning very late to the marriage again than he should be. I am no attorney but all these points i think could point to a very good circumstantial evidence and a very good motive to put him behind bars.