Polkey could be relevant in relation to the procedure followed (if they can show that the outcome would have been the same even if the correct procedure had been followed). However, Polkey may not be relevant when it comes to the redundancy situation itself and whether your job was no longer needed.
One example of fair redundancy is where the same amount of work remains but fewer employees are needed to do it (this can include consolidation of jobs by spreading out certain duties amongst existing employees). A like for like replacement is unlikely to qualify but if it was a case of it being taken over by the owner, someone in charge of the business, who cannot themselves be replaced, then it can create a viable case.
In any event, before a person can make a claim in the employment tribunal, they would be required to participate in mandatory early conciliation through the Advisory Conciliation and Arbitration Service (ACAS).
The purpose of this process is to allow ACAS to mediate between the claimant and respondent to agree on an out of court settlement in order to avoid the need for legal action in tribunal. The respondent does not have to engage in these discussions, or if they do and the talks are unsuccessful, the claimant will be issued with a certificate allowing them to make a claim.
However, if a settlement is reached, the claimant would agree not to proceed with the claim in return for the agreed financial settlement. Other terms can also be agreed as part of the settlement, such as an agreed reference.
To initiate the conciliation procedure ACAS can be contacted online by filling in the following form (https://ec.acas.org.uk/Submission/SingleClaimantPage), or by phone on 0300(###) ###-####