Metropolitan Police Deputy Assistant Commissioner Neil Basu said the arrest was "significant, but the terror threat level remains at "critical".
May said military personnel would take over guard duty at certain closed "protected sites", freeing up 1,000 police officers to be deployed on the transport network and on streets across Britain.
"This arrest will lead to more activity from our officers", he continued.
Police said a hunt involving hundreds of detectives backed by the intelligence services was underway to find out who was responsible. However, and to re-iterate, there is no information to suggest that events in London are linked in any way to Jersey.
An 18-year-old man has been arrested in connection with Friday's bomb attack on a London subway train.
"Although we are pleased with the progress made, this investigation continues and the threat level remains at critical", he added.
British authorities announced they were treating the incident as a terror attack. Ambassador to London Antonio Lagdameo said they are continuously monitoring the situation.
Witnesses described seeing a fireball filling the carriage, with passengers suffering burns, as well as other minor injuries during the rush to escape.
"The rationale behind this request is to reduce numbers in crowded areas and will be applicable to all public events taking place this weekend". But it was the only one in 2017 in which nobody died.
"So it's great news that the Kiwi.is not seriously injured".