Your employer cannot dismiss you simply because of your wife's misconduct. If you are being asked to leave simply because of your wife’s misconduct, you can bring an unfair dismissal claim at an employment tribunal, provided you have at least two years’ service.
If you do not have this length of service, you could still bring a claim for breach of contract, but if you bring this kind of claim, your compensation will be limited to just your notice pay and any sums you would have earned if you had been allowed to work your notice.
If a single worker in a relationship with a colleague would not have been asked to leave in the same circumstances, you may also be able to claim marital status discrimination, regardless of how long you have worked for your employer, but this is likely to be a tricky claim to win.
Seek advice first from your union rep if you have one, or from a solicitor. In-house mediation may be another way of encouraging your employer to see sense. Mediation is voluntary. Acas and the TUC have put together a joint guide to mediation for trade union reps that you may find helpful.
Hopefully, your trade union can help you solve the problem without you losing your job or paying out huge sums in legal fees.