In a statement Tuesday, authorities said they arrested a 27-year-old man Tuesday morning.
A Metropolitan Police spokesman said the search for Thomas continued on Wednesday.
The three attackers were shot dead by police Saturday night after they drove a hired van into pedestrians on London Bridge and then stabbed people in the nearby Borough Market, leaving seven people killed and 48 injured.
The three terrorists carrying out Saturday night's attack were shot dead by police within eight minutes of the alarm being raised.
But an announcement - made before the Manchester and London Bridge attacks - that they planned to make some of the elderly pay more for their care saw that lead start to shrink, to between one and 12 points now.
Twelve other men arrested in the early stages of the investigation have all been released without charge.
Jobless rate in London jumps above 6%
Nationally, the jobless rate went up slightly to 6.6%, despite the economy adding a net total of 54,000 jobs. The increase in unemployment was due to the entry of 78,400 Canadians into the labor force in May.
Two of the men, aged 27 and 29, were held on suspicion of preparing acts of terrorism while the third was detained over suspected drugs offences.
In fact, Butt was one of the main characters in a television documentary called The Jihadis Next Door.
In a statement, her family said: "We are deeply saddened at the tragic loss of our attractive daughter and sister of Harrison and Scott".
Butt and Redouane, who also used the name Rachid Elkhdar, lived in Barking, while Zaghba is reported to have worked in a restaurant in London.
Earlier police, who were hunting for 45-year-old Frenchman Xavier Thomas, missing since the attack, said that they had found a body in the River Thames. He said eight other French citizens were wounded. As well as carrying knives, the attackers wore fake suicide vests, created to spread more fear.
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