Thank you for your quick replies, I appreciate it. The value of the base resistor is 10k ohms. I just checked with a multimeter and the ground does not go to 0.0V when the transistor is turned on. It goes to 0.184V and I think that is the problem.
The relay part# is KUHP-11DT1-12.
I'll try to explain it better, I have a transistor which first switches on an LED. The same connections of this transistor go to another transistor which turns on the relay. I am doing this because the relay requires 12V to turn on and the LED one uses 5V.
Now, for the LED transistor, ground goes to 0.184V and not 0.0V. The circuit has already been milled and therefore difficult to change. Therefore, any changes I have to make will have to be made on the the transistor circuit for the relay. I hope that makes things a bit clearer.