Yes, privacy may be a factor and parishioners should expect privacy during the services. The church is located at Sandringham, but it's still a working church and should be respected as such.
It seems to me that the vicar was petty in this case. The consultant sounds as if he/she was highly biased in favor of the vicar's views/wishes. Turning to the King was a power move. Yes, the King is the Head of The Church, but the Bishop of Norwich should handle the dispute, he should have appointed entirely neutral people to investigate the dispute and reach conclusions. It's sad for everyone, the Choir Director was pushed out, the vicar used power moves.
This stuff happens with ministers, rabbis, priests, there's disputes with the parishioners vs. the clergy or other parishioners, it's human.
At my church we've had 3 dust ups over the last 6-7 yr. and it's been the 4-5 extremely wealthy families in the parish who think they can run the church. They've managed to oust 3 Associate Priests, because they weren't "up to our standards". The story going around in our poor section is they didn't like what they were told by the priests in Confession....as I said it happens everywhere and it's sad. It can divide the congregation and cause people to leave the parish plus new members are reluctant to join because of what they've heard or read about the parish.