That document is dreadful; it's full of half truths and doesn't actually say what has happened. It needs to be withdrawn before everyone gets the wrong idea.
What we have lost is access to the EGNOS Safety of Life (SoL) service which is a pre-requisite for LPV approaches. However, the EGNOS Open Service (which is free) is still available so your GPS will still get a useable SBAS augmentation signal. This means that LNAV, LNAV+V and LNAV/VNAV (using SBAS for vertical guidance) will continue to be available. The CAP fails to mention nearly every aspect of that.
Practically at most airports you won't see much difference. Indeed at Cardiff the LPV and LNAV/VNAV minima are nearly identical. At some places where the LNAV/VNAV minima weren't included then the difference from LPV to LNAV minima is bigger - possibly up to 3-400 feet.
But it's the potential of LPV to replace Cat I ILS that we have lost. The Channel Islands had some of the only LPV 200 approaches in the UK but these should have been at every instrument airport by now. Hopefully someone pulls their head out of the sand at UK plc and renegotiates access to the SoL.