My reading of the CAA words is this;
If your private licence permits you to fly aeroplanes up to 5.700 Kg then you may continue to do so using a 'Self Declaration'. [a National and an ICAO PPL limit]
If your private licence limits you to fly aeroplanes up to 2000 Kg then you may continue to do so using a 'Self Declaration'. [a NPPL and LAPL limit}
In other words the Self Declaration does not change you licence private privileges for flight within the UK airspace: It is also usable with an IMC and and a Night rating. However, the Self Declaration does not support the IR.
The UK LAPL for the moment is now superfluous, because we already have the NPPL and the LAPL adds nothing more, but the CAA is yet to make an announcement on its future.