Nope, not for a private vehicle.
Minibusses do now have a tyre age requirement following a fatal RTA caused when a minibus stopped after 30+ year old tyre failed & was hit while on the hard shoulder by a HGV. Also applies to front tyres of HGVs.
I was very suprised at this, as I was going to suggest taking the matter up with DVSA given the age & state of the tyres on the VW that had just passed an MoT. But I could not find anything in the MoT testing requirements that had been contravened. Cracks only fail if the cords are visible, which they were not.