The annual detection rate in 1996-97 increased by 7.5 per cent to 24.3 per cent, with nearly half of violent crimes being solved.
The results were "impressive" and had been achieved by a "concerted police effort in partnership with the railways, local police and communities", said BTP Chief Constable Desmond O'Brien.
The statistics relate to reported crime on main-line railways, as well as London Underground and the Docklands Light Railway.
The only category of crime to show an increase was sexual offences, which rose 11.9 per cent in 1996-97. However, more than two in five of these cases were detected.
Violent crime fell 1.5 per cent, criminal damage was down 13.1 per cent and line of route offences (such as obstructing the line) fell 8.9 per cent.
"It is always dangerous to take one years' statistics in isolation but these results reflect a downward trend, with reported crime on the railways down 20% since 1990," said Mr O'Brien.