Certainly one possible cause and a cheap and easy one to check and if needed fix. Sprint oil fill is a square head on the left hand side just under the clutch slave cylinder, fill to it just dribbles out. If you have no idea when the oil was changed, would not hurt to drain and refill, there's a handy drain plug at the bottom. EP90 GL4 oil, or if you're feeling adventurous and wish to use a modern oil then I use Millers TRX 75w90 in gearbox and diff.
edit: Whoops, took a call before clicking submit and I've doubled up with the good advice already given!
Current fleet: '75 Sprint, '73 1850, Daihatsu Fourtrak, Honda CG125, Yamaha Fazer 600, Shetland 570 (yes it's a boat!)
Past fleet: Triumph 2000, Lancia Beta Coupe, BL Mini Clubman, Austin Metro, Vauxhall Cavalier MK1 & MK2, Renault 18 D, Rover 216 GSI, Honda Accord (most expensive car purchase, hated, made out of magnetic metal as only car I've ever been crashed into...4 times), BMW 318, Golf GTi MK3 16v x 3