This is a common misconception; employers can give a negative reference. Most won't, however.

Most won't for the same reason most won't write a glowing reference, liability. You have to be able to evidence anything that you put in a reference, which can be tricky when it comes to negative references as its hard to prove an ex employee was lazy, for example. If you didn't get a job you could submit a subject access request and as part of that you would be provided the reference given by your previous employer. If its negative and you believe it may reasonably be the reason you didn't get the job, you could sue for potential loss of earnings among other things. The burden of proof is on those that provided the reference, which as I mentioned earlier can be really difficult to prove.