Julian Scarfe wrote:

10ish years after overlay GPS approaches were introduced in the US, we in
the UK still have no GPS approaches. There must be a considerable body of
evidence collected on accidents, incidents and anomalies over the period
that GPS approaches have been in use. In particular, there may be evidence
that GPS approaches have improved overall safety in non-precision
approaches.

Any pointers please?

No pointers. Emprically, I'd say they are working great in the US. The issue
is politics, not safety.