I used to have it on an old 78 of my grandad's, but I can't for the life of me remember who sang it. The name may have been Jack something.

There was the verse given above, which starts "In our little village ...", then the chorus "Mary Ellen at the church turned up..."
then another verse:
"The people waiting at the church, they nearly blocked the road
They were waiting in the road for the money the bridegroom owed.
"My heart is broken!" cried the bride, so Jim - the butcher's son -
rushed into the shop and brought her out another one.

Mary Ellen at the church turned up..." etc

The song was just called "Turned Up."