Since they had to have a very public wedding, I completely understand wanting something intimate just for themselves, even if it was not official (something they could have made clearer in the interview).
What is standard practice is for the clergyman to visit the couple in their home ahead of the marriage and get them to practice the vows so they are not overcome with emotion on the day. It can be an emotional moment - often people cry - but it’s not a wedding. Sometimes the clergy will pray for the couple at the end of it etc so it can feel quite formal. Simple Services of Blessing and dedication for marriages are available with the CofE but normally should occur after the legally binding event.
When the rehearsal is in a church and the witnesses are present, the vicar will cut off the couple before the saying of the crucial parts to ensure they are not legally married before the day. Normally, people are that careful about process.
I just presumed that M&H were overstating this standard rehearsal exercise but who knows. Maybe Justin Welby was so star-struck he was willing to do anything for H&M - it’s quite possible .
An extra technicality is that CofE’s are licensed to issue wedding certificates but if you get married in another approved venue (like a Methodist church or country house with an officiant), the route to obtaining your paperwork and publishing bans is different. If not in the CofE, you have to notify your registry office x amount of time ahead and they publish the bans of marriage etc... after a certain period you then have to collect the paperwork and hand it to your licensed venue ahead of the day.
If you’re getting married in a CofE building, the church simply needs to read the bans I think 3 weeks in a row.
I guess the CofE can’t respond here. Either they have to come out and accuse H&M of lying - "it was clearly just a rehearsal and I'm not sure why they referred to it as a private wedding, there was never any ambiguity" - which would cause a backlash against them in terms of public reaction, or admit Justin Welby did something completely illegal which should lead to his resignation and wouldn't reflect wonderfully on them either.
There are really strict rules about weddings in the CofE which are taken very seriously by vicars (and generally in the UK, private weddings are not allowed full stop - only licensed venues) and during the past year, to comply with lockdown rules as well as their own, some churches had the couples marry on the doorstep and the small number of guests sit outside in the church courtyard. Not all churches allowed that and many couples were denied the opportunity to use outside space at all.
There has been quite a lot of talk this year in the British press to allow a loosening of the rules because of the impossible situations created by **** Many couples have not been able to marry at all because private ceremonies are illegal.
The context means H&M’s comment has attracted more interest.