In the UK, there is no specific time limit set by law for how long employers must keep copies of payslips. However, it is generally recommended that employers keep records of payslips for at least three years.
This recommendation is based on the Limitation Act 1980, which sets a general time limit of six years for bringing a breach of contract claim. Since a payslip is a record of an employment contract, it is advisable for employers to keep them for at least six years in case an employee makes a claim related to their pay during that time period.
Furthermore, employers are required by law to keep records of their employees' pay, tax, and National Insurance contributions for a minimum of three years, so it makes sense to keep payslips for at least that long.
It's worth noting that if an employee requests copies of their payslips, employers must provide them within a reasonable time frame. If your emplayer making dely in Providing Replacement Payslips then order Replacement Payslips Online