There were 1,117 sexual offences recorded by British Transport Police (BTP) in the 12 months ending March 2014, a near-21 per cent increase on the 925 in the previous year.
Most of the increase was in sexual crime against girls and women, which which went up by 139 to 624. Indecent exposure cases rose from 141 to 148.
A BTP spokesman said the rise in sexual offences was slightly higher than seen by other UK police forces.
He added: "Part of this increase can be attributed to the high-profile prosecutions of celebrities for historical offences which have, undoubtedly, given victims more confidence to come forward."
Covering Scotland, England and Wales, the BTP figures showed that overall for 2013/14, notifiable crime - the more serious offences - dealt with by BTP, fell by 5.7 per cent from 53,885 to 50,840.
BTP Chief Constable Paul Crowther said the force's Project Guardian had had a significant impact on sexual offences .
Project Guardian is meant to increase awareness and confidence among the public to report unwanted sexual behaviour to police .
Motor vehicle and cycle crime as well as public disorder offences dealt with by BTP rose slightly, but there were drops of around of 17 per cent in thefts of passenger property and robberies, with thefts of railway property falling nearly nine per cent to 4,406.
BTP attributed the dip in thefts to its Operation Magnum campaign advising passengers on tactics used by thieves.
The force also pointed to its efforts in tackling metal and cable theft from the railways.