Limited liability has the effect that you cannot sue the individual who wrote the cheque, but you are perfectly entitled to sue the company in question.
You would sue on the back of the cheque, and since it would be for a liquidated sum the process would not take long at all.
As the case would be in the District Court the cost of this should not be too much.
There would also be a good chance that the initial letter from your solicitor demanding payment within 7 days would cause them to pay you to avoid the expense of having to deal with a court appearance, interest and judgment.