A significant proportion of UK employment law is derived from European Directives (TUPE, Collective Redundancies, Working Time and Agency Workers rights to name but a few). There was a thought that Brexit would potentially mean a bonfire for some UK employment laws but it's fairly clear (as clear as things can be when it comes to Brexit) that the status quo will be maintained, not least because of the disruption wholesale changes would cause for businesses if new employment laws were introduced.
The Government has pledged that there will be 'no regression' for UK employment laws but that doesn't mean there will be harmonisation with our European counterparts. There may be some changes in the future, but at the minute all eyes, from an employment law perspective, are firmly on immigration.
While the UK pledges to maintain “high regulatory standards” for environment, social and employment law, it stops short of the harmonisation the EU expects from single-market participants.