Three other people were arrested in Tottenham, north London, at the same time as McLoughlin, police said.
The 54-year-old man from Tottenham, 45-year-old woman from Edmonton, north London, and 50-year-old man from Hackney were arrested on suspicion of assisting an offender.
All four are being questioned at Hatfield police station, Hertfordshire Police said.
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A lamp in the tower which houses Big Ben is to be switched off for the first time in more than 70 years.
Sir Bruce entertained audiences for more than seven decades.
Work in the tower will also pause over the bank holiday weekend.