Police were first called to reports of a woman being sexually assaulted on a Bakerloo line train at Harlesden station on September 5, at around 4.4pm.
Soon afterwards, police heard of two more women sexually assaulted on a Thameslink train and the platform at Blackfriars station.
According to the British Transport Police, a woman was then attacked on a Thameslink train towards St Pancras station at around 6.40pm and then a woman was targeted at West Hampstead Thameslink station at around 7pm.
The force believes that these incidents are linked.
An arrest has been made and further enquiries are ongoing.
Potential witnesses or people who may possibly have been a victim themselves are asked to come forward.
Anyone with information can contact BTP on 61016 or call 0800 40 50 40, using the reference 656 of 5 September. Alternatively, contact Crimestoppers anonymously on 0800 555 111.
