This is the case whether travellers are vaccinated or not. The Passenger Locator Form is no longer needed for arrivals after 4am on Friday 18th March in these three countries. The announcement can be found on the UK.gov website here. The Wales website does not yet indicate any change to travel rules, although it is probable they will follow suit.
France has also now dropped the requirement to have a negative Covid test result for the return journey back to France and, from 1st July, it appears that a vaccination certificate is no longer requested - even though the French Interior Ministry's website still states it is required. Go to the Covid-19: How it affects your travel between France and the UK page of this website for more information.