A 30-year-old man was arrested in Birmingham on Sunday on suspicion of preparing terrorist acts.
He is the 12th person to be arrested in connection with the investigation. Nine others have been released without further action.
Another 58-year-old man, 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.
Fourteen searches have now concluded, with one ongoing in Birmingham.
Masood drove his car along the bridge at speed, mowing down pedestrians.
He was shot dead by police after he stormed the parliamentary estate on Wednesday afternoon.
Counter-terrorism officers have spent days piecing together what led the 52-year-old to shed his birth name and later unleash carnage on the capital.
Police said they now believe the knifeman acted alone but that understanding why he did it may have died with him.
It has since emerged Masood used messaging service WhatsApp seconds before launching the attack on Wednesday 22 March.
But because messages are encrypted, agencies are unable to see what was said.
She also left the door open to changing the law if necessary.
Her stance has been criticised by technology experts who said there were serious legal, ethical and practical obstacles to offering security agencies a "back door" to view encrypted messages.
Many wore blue to symbolise hope as they stood holding hands for five minutes as Big Ben chimed 4pm.
People from a range of backgrounds joined the event organised by Women's March On London.