The following assumes you are a contractor to the company, and not an employee.
A claim for repayment of a debt through the court will be slow. Once you have sent your pre-action letter and have given the debtor reasonable time to respond, you then serve the claim form. The other side can request an extension so that it has 28 days to serve its defence. You are allocated a date for the hearing after that. Once you have your judgment, you then have to start enforcement proceedings if the debtor does not pay.
Time is of the essence when a company is struggling to pay its creditors.
Winding-up petitions do generally spur reluctant payers into action - provided of course that funds are available. Note however that if there are any secured creditors that have enforced their security, those assets will not form part of the assets available on liquidation. The same applies if a secured creditor enforces after the presentation of a winding-up petition: the secured creditor can apply to the court to stay the winding-up (at least in relation to its security) and this is granted as a matter of course: it is illogical that an unsecured creditor should receive payments ahead of a preferred creditor.
But bear the following in mind: Winding-up proceedings are only appropriate in circumstances where the debt owed to the creditor is not disputed. Winding-up proceedings are not the appropriate forum in which to decide disputed issues of fact. A statutory demand which is presented in relation to a disputed debt (or a debt where the company has a genuine right to set-off or cross-claim) is liable to be set aside on the application of the company, and a winding up petition presented in such circumstances will be dismissed.
You can check whether a winding up petition has already been presented against the company. This may be done by a search of the Central Registry of Winding up Petitions by telephone (0906 754 0043).