"...pleaded guilty to causing a nuisance without reasonable excuse"

thats a crime?

https://en.wikipedia.org/wiki/Public_nuisance

The nuisance action began in twelfth century England as a criminal writ, belonging only to the Crown. It was used in cases that involved encroachments upon the King's land or the blocking of public roads or waterways. The King sought to punish these criminal infringements, commonly known as "purprestures", through criminal proceedings. Over time, activities prosecuted as public nuisances included everything from embezzling public funds to having a tiger pen next to a highway, from assisting a homicidal maniac to escape to placing a mutilated corpse on a doorstep, and from selling rotten meat to "subdividing houses to the point where they become 'overpestered' with the poor". As these examples demonstrate, early authority to commence public nuisance actions was derived from the sovereign's "police power".[10]

Spencer (1989 at 59) describes the offence as "a rag-bag of odds and ends which we should nowadays call 'public welfare offences'".[11] But the common feature of the crime is that members of the public suffer a common injury through interference with rights which they enjoy as citizens. The modern definition is found in paras 31–40 Archbold (2005):

A person is guilty of a public nuisance (also known as common nuisance), who (a) does an act not warranted by law, or (b) omits to discharge a legal duty, if the effect of the act or omission is to endanger the life, health, property, morals, or comfort of the public, or to obstruct the public in the exercise or enjoyment of rights common to all Her Majesty's subjects.[12]

can we arrest trump for that if he comes back to the uk?

I'm pretty sure that national leaders don't normally visit countries unless they are extended diplomatic immunity, so probably not.

EDIT: Hmm. Though...this says that it was abolished as a crime in England and Wales four years ago. There's still the tort, but the way The Mirror described it, he was "fined", and I think that you only get fined in criminal law, not civil law (in civil law, the analog would be called paying punitive damages, at least here in the US).