I don't know if this helps.... but some friends of mine were in a similar situation. The extended family was similarly not aware they were already married (although the parents were in on the plans all along). They got married in the States legally in a courthouse for visa purposes, but due to religious reasons, waited until they had the 'God sanctioned' religious ceremony in Britain before they considered themselves properly married.
My dad, who is a pastor in the States (and who got permission to marry me legally in Scotland btw!), 'officiated' at the religious ceremony. No papers were signed, but oaths were exchanged as if it was the REAL ceremony (and to them, it absolutely was). The ceremony was in the ruins of Whitby Abbey, and it was absolutely lovely.
As far as I am aware, there is no law against this. They could ask a friend who is a pastor or priest (or humanist minister, or buddhist monk, or druid, etc!) to officiate at a vow exchange ceremony, and as long as official papers are not applied for and signed, I do believe it's all above board.
However, I do agree the family really ought to be told, as I can't imagine it's good karma to start a marriage on a falsehood... but if this is not going to work, the family doesn't ever have to know, I suppose.
