Is the starter a roundy-thingy (technical term...) that sticks out a bit .
"Be careful, power off the light fitting first"
YES, it's a cylinder, 20mm diameter, 40mm length(approx) with 2 pins sticking out at the end (the end you can't see). Catch the end that you can see (between thumb and forefinger) and turn it anticlockwise, it should drop down to you. Take it to your local friendly electrical wholesaler and a new one should cost less than a euro.
Of course if you are in rented accomodation I would expect the landlord to sort out this for you!