The terror threat level has been reduced as fresh arrests and raids have been carried out linked to the Manchester suicide bombing.
Troops will be gradually withdrawn from the streets from Monday onwards, having been drafted in to bolster police numbers, the Prime Minister said.
The Joint Terrorism Analysis Centre (JTAC) increased the threat level to "critical" - its highest level - meaning a further terror attack was considered "imminent".
It has now been reduced to "severe", meaning a further assault is "highly likely".
Speaking after a meeting of the government's Cobra emergency committee, Mrs May said the decision had been taken after "a significant amount of police activity" over the last 24 hours.
She said: "The public should be clear about what this means - a threat level of severe means an attack is highly likely. The country should remain vigilant."
The massacre at the Manchester Arena carried out by Salman Abedi, in which 22 people were killed, was the worst terrorist atrocity to hit Britain since the July 7 attacks in London in 2005.
The terror threat had been at critical for the first time in a decade.
Mrs May also said Operation Temperer, allowing the military to be deployed to protect key sites, will be rolled back after the Bank Holiday.
She said: "To provide maximum reassurance to the public Operation Temperer will continue to operate until the Bank Holiday concludes.
"Then from midnight on Monday onwards there will be a well planned and gradual withdrawal of members of the armed forces who will return to normal duties."
The news was announced as police evacuated an area of Moss Side in Manchester as fresh arrests and raids are carried out linked to Monday's suicide bombing.
A property was being searched as Greater Manchester Police attempt to close the net on the suspected terror network behind attacker Salman Abedi.
Officers were said to have been taking precautionary measures to ensure public safety.
Two men aged 20 and 22 have been held on suspicion of terror offences after officers used an explosive device to gain entry to a property in the Cheetham Hill area of the city.
The operation in the early hours of Saturday morning brings the number of suspects being held in custody to 11.
The development came as a vast security operation gets under way to protect hundreds of spring bank holiday events across Britain this weekend.
As the public was urged to carry on with planned activities against a background of heightened security fears:
* More than 1,000 armed police are on standby as major spectacles, including the FA Cup Final at Wembley and the Premiership Rugby Final at Twickenham, are expected to draw tens of thousands of people into public spaces on Saturday.
* Metropolitan Police Assistant Commissioner Mark Rowley said "immense" progress had been made in the probe into the associates of suicide bomber Salman Abedi and a "large part" of his suspected network had been dismantled.
* US singer Ariana Grande vowed to return to Manchester to play a benefit gig for fans caught up in the blast.
GMP said officers made the latest arrests as they executed a warrant at an address in Cheetham Hill, north of the city centre.
It followed searches at a separate property in Cheetham Hill and an address in the Longsight area in south Manchester.
Residents described hearing a "loud bang" as the latest raid and a controlled explosion took place in Brideoak Street in Cheetham Hill..
Shakufta Bi, who lives across the road, said the noise woke her in the early hours and she saw the street full of police cars and vans along with men in green military uniforms.
Mrs Bi said a Libyan family live at the address - a mother, three sons in their late teens or early 20s and a daughter. The father, an engineer, lives in Dubai and visits occasionally.
All the sons pray at a mosque 200 yards away, known locally as the "Libyan" mosque.
Some neighbours report seeing the sons wearing both "western" dress and traditional Islamic robes.
Another neighbour, Val Jones, said: "I heard a loud bang, it sounded like a door getting kicked in. Then I looked out the window. I seen a lot of police going to the bottom end then I seen a convoy of cars, just normal, private, unmarked cars from the bottom of the street to maybe where that taxi is.
"Car doors flew open, police come out, soldiers in combat gear come out (wearing) green body armour.
"They were just walking up and down the street with guns, focusing (on) ... I don't know which house it was but it was pitch black at that time.
"I knew it was serious but I didn't know it was anything. I thought it was a drugs raid or something like that. You hear a lot of that around here."
On Friday evening, a 44-year-old man was arrested in the Rusholme area of the city. Witnesses reported seeing armed police storm a bus on its way to the town centre at around 7pm.
Twenty-two people, including seven children, were killed and scores injured when Abedi launched a suicide attack at Manchester Arena on Monday night.
The Duke of Cambridge and Labour leader Jeremy Corbyn are expected to head to Wembley on Saturday.
In Hull, US star Katy Perry will perform amid tight security at Radio 1's Big Weekend, while in Manchester, armed officers will patrol The Courteeners' concert at Old Trafford cricket ground, where fans were warned extra security checks will be in place.
On Sunday, the Great Manchester Run will go ahead as planned, with defiant runners and spectators due to turn out in large numbers as the city recovers from the atrocity.
Activity in the Manchester probe is expected to continue throughout the weekend and investigators remained at at least 12 locations across the North West on Friday evening.
The bomb disposal lorry left Yew Tree Road and the cordon was lifted shortly before 12.30pm with residents filing into the streets.
Latest figures from NHS England show that 63 people injured in the blast are being treated in hospital with 20 in critical care.