Two men remain in custody over the Westminster attack as encrypted messaging services such as WhatsApp faced criticism for potentially allowing terrorists to communicate undetected.
Killer Khalid Masood is reported to have used the app seconds before mowing down pedestrians at speed and storming the parliamentary estate armed with two knives last week.
The Home Secretary called for the encrypted networks to build back doors into their system so security services can access terrorists' messages during investigations.
Amber Rudd said she supported end-to-end encryption, offered by the likes of WhatsApp, but said security services must be able to eavesdrop on messages when they have a warrant.
Although such encryption makes it difficult for investigators to establish whether Masood was talking to an accomplice before Wednesday's rampage, which left four dead, police said they believed he acted alone.
A 30-year-old man was arrested in Birmingham on Sunday on suspicion of preparation of terrorist acts, making him the 12th person to be held over the deadly plot.
Another man, 58, also arrested in Birmingham, remains in police custody after a series of raids across the country.
Officers have carried out a total of 15 searches at various addresses in east London, south London, Brighton, Surrey, Carmarthenshire, Birmingham and Manchester.
On encrypted messaging services, Ms Rudd told BBC One's Andrew Marr Show on Sunday: "It is completely unacceptable, there should be no place for terrorists to hide.
"We need to make sure that organisations like WhatsApp, and there are plenty of others like that, don't provide a secret place for terrorists to communicate with each other.
"It used to be that people would steam-open envelopes or just listen in on phones when they wanted to find out what people were doing, legally, through warrantry.
"But on this situation we need to make sure that our intelligence services have the ability to get into situations like encrypted WhatsApp."
WhatsApp said in response that it had been assisting the police investigation.
A spokeswoman said: "We are horrified at the attack carried out in London earlier this week and are co-operating with law enforcement as they continue their investigations."
Counter-terrorism officers have spent days piecing together what led Masood, 52, to shed his birth name and later unleash carnage on the capital in an 82-second spree.
The Muslim convert was shot dead by armed police after fatally knifing Pc Keith Palmer in the Palace of Westminster's cobbled forecourt.
On Saturday afternoon officers searched a maisonette in Bredon Croft, Hockley, Birmingham, where friends of Masood lived.
A family living next door said Masood used to come wearing Islamic dress and take their neighbours' children to the mosque.
One of the mothers at nearby Brookfields Primary School said her daughter was best friends with Masood's, but added: "I always got the chills from him."
Sabrina Hussain said she changed her mind about taking her child, nine-year-old Skye, to his daughter's birthday party just before Christmas.
"I thought I was being a bit over-protective, but then I just thought, 'No, I can't let her go' and we turned the car around and I made up an excuse saying the party had been cancelled," Ms Hussain, 28, said.
"I just didn't want her to go.
"There was just something about him that wasn't right."
Masood's victims included US tourist Kurt Cochran and his wife Melissa who were on the last day of a trip celebrating their 25th wedding anniversary.
Mr Cochran was killed and Mrs Cochran was badly injured.
Aysha Frade, believed to be a 43-year-old married mother of two, also died, along with retired window cleaner Leslie Rhodes.
Dozens of other people were injured in the attack which has prompted acts of tribute and solidarity across the UK and worldwide.
The Home Secretary left the door open to changing the law over access to social media networks if necessary.
But she said she would rather see an industry-wide board doing it independently, as the best people to take action are those who understand the technology and the "necessary hashtags".
Ms Rudd said she was calling in a "fairly long list" of relevant organisations for a meeting on the issue on Thursday, including social media platforms.
"I would rather get a situation where we get all these people around the table agreeing to do it," she told Marr.
But her call for access was branded "draconian" by one former Metropolitan Police deputy assistant commissioner.
Lord Paddick said: "The real question is, could lives have been saved in London last week if end-to-end encryption had been banned?
"All the evidence suggests that the answer is no."