This is the area where the law most often surprises people, and where the deadline is shortest. The police generally do not owe a duty of care in negligence for failing to investigate. The route that works is a different one.
Why negligence usually fails
A line of authority running from Hill v Chief Constable of West Yorkshire [1989] AC 53 through to Robinson v Chief Constable of West Yorkshire [2018] UKSC 4 holds that the police do not owe a general duty of care to individual members of the public in the investigation and suppression of crime. Robinson narrowed that considerably where officers cause injury by a positive act, but for a failure to investigate the position largely holds.
The route that does work
The Human Rights Act 1998 is the effective route. Articles 2 and 3 of the European Convention carry an investigative duty, and in serious cases a failure to investigate properly breaches it. In Commissioner of Police of the Metropolis v DSD and NBV [2018] UKSC 11, the Supreme Court held the Metropolitan Police liable under Article 3 for serious investigative failures in the John Worboys case, and awarded damages.
"Proceedings under subsection (1)(a) must be brought before the end of the period of one year beginning with the date on which the act complained of took place; or such longer period as the court or tribunal considers equitable having regard to all the circumstances."
Human Rights Act 1998, section 7(5)Which limitation period applies to your situation depends on how the claim is put, and a claim can often be put more than one way. Treat this as urgent and get your own position checked rather than working from a general page.
The free routes
A complaint to the force costs nothing, and if the answer does not stand up you can apply for a review. Across all forces reporting, close to one in four completed reviews found the force's own outcome was not reasonable and proportionate. Where a victim of crime is unhappy with how a case was handled, the Victims' Right to Review scheme is a separate and free route.
How long you have to bring a claim
Publishing a general figure here would be worse than publishing nothing, because a reader who relies on the wrong one loses their claim outright. Get your own position checked, and do it early rather than late.
The free routes, before any claim
A complaint to the force costs nothing and does not stop you claiming later. If the force's answer does not stand up you can apply for a review, and across all forces reporting, 24.5% of completed reviews found the force's own outcome was not reasonable and proportionate.
The three routes, and what each one gets you.
Start with your force
Complaint handling, review outcomes and stop and search practice vary enormously between forces. Every force has its own page here with its own figures.