Not all employment-related cases go to a tribunal. Some cases go to the civil courts (the small claims, county, or high court).
For example, if you do not have enough service (two years for most claims) to claim unfair dismissal in the employment tribunal, you may want to bring a claim instead for your contractual notice in the civil courts. This type of claim is known as ‘wrongful dismissal’.
Sometimes, unions bring this kind of claim using a few members who agree to act as representative litigants. If the claim succeeds, the result can impact on co-workers who share the same contract term.
Sometimes, unions help to coordinate 'class actions', which can involve hundreds of litigants.
Civil courts can also hear claims for personal injury (i.e. if you are injured in the workplace or suffer ill-health as a result of your working environment and want to sue your employer for damages). In general, employment tribunals do not award compensation for personal injury. (Discrimination claims are an exception.)
If you are a union member, your union may have arrangements in place with a firm of specialist lawyers, enabling the union to cover your legal costs as long as your claim meets set criteria (such as having good prospects of success).
If you are not in a union, and don't work in a unionised workplace, a local advice agency may be able to recommend solicitors who specialise in personal injury cases.