Hidden away deep in an AIC there is admision that GPS aproaches are leagal in UK registered aircraft provided the GPS in the aircraft has the aproach in the data base
The AIC isn't the ANO
We could start another discussion on this... It is just like the IMCR minima being the IR minima increased to 500/600ft - most likely a CAA advisory thing but not law.
On a UK private flight, one can do a DIY instrument approach in any way one wants to. A 100% GPS instrument approach is 100% legal, and a fair number of people do just that - they just don't talk about it.
If I had my own farm strip, with no nearby hills, I would do them too. But I would probably put up an NDB, activated by a SMS message and turning itself off after 20 mins