Wrongful dismissal only concerns your employment contract and whether your employer has dismissed you in breach of it. There is no consideration on whether the dismissal was “fair” (See unfair dismissal page for this). The focus is purely on whether your employer breached a term of contract of employment. Most commonly, it may refer to whether you’ve been dismissed without notice, or with less than the stated (within your contract or statutory) minimum notice period.
The statutory minimum notice period cannot be less than one week for each year of your service with your employer, and is capped at 12 weeks. For your employer to dismiss you without breaching the terms of your contract, they need to give you advance notice of your termination, and for it to comply with statutory terms or the terms within your contract.
In some instances, an employer may pay a dismissed employee in lieu of notice, rather than permitting them to work their notice period. Paying in lieu of notice is more than often accepted as damages for these claims. This payment would not be classed as a breach of contract and would not likely hold up as grounds for a wrongful dismissal claim.
However, if the employee’s contract did not include the right to terminate by issuing a payment in lieu of notice, they could still bring a claim.