Hi Susan,
It's an interesting marriage! Marriage by declaration, and they forgot to sign the register, so their names were filled in by the registrar

One hopes he got it right

Okay, here's a feeble try, just so you know you're not alone in your frustration... On the marriage cert Ella is said to be from "Lough Tummel". After a good deal of poking around I decided that must be something like Loch Tummel in Perthshire.
Please anybody correct me if I'm wrong!!! I'm only guessing! So, in 1881 I searched for John, a mason, married to Margaret and living in Perthshire. Here is one such, with a connection to Haddington:
1881
Main Street, Kilmadock, Perthshire
John McBeth, 31, Head, born Kilmadock, Perthshire, Mason
Margaret McBeth, 32, Wife, born Dirleton, Haddingtonshire
Duncan McBeth, 1, Son, born Kilmadock, Perthshire
However, I can't find that this couple ever had a daughter anything like Ella... but it was nice for a moment
There is also an Ella McGregor, born in London, age 9 in the 1891 census for Little Dunkeld, Perthshire. Her mother is possibly Margaret. Since that was Ella's mother's maiden surname, it caught my attention.
1891
Brich Cottage, Little Dunkeld, Perthshire
William McGregor, 71, Head, born Old Machar, Aberdeenshire, Woollen Manufacturer
Annie McGregor, 46, Daur, born Alloa Clackmannanshire
Margaret McGregor, 27, Grandaur, born Kincardine, Perthshire
William McGregor, 11, Grandson, born London, Middlesex, Scholar
Ella McGregor, 9, Granddaur, born London, Middlesex, Scholar
Susanna McGregor, 6, Grand Daur, born London, Middlesex, Scholar
Eliza Melville Hutchison, 21, Visitor, born Perth, Perthshire
Jemima Hutchison, 16 Visitor, born Perth, Perthshire, Scholar
Robert Menzies, 52, Servant, born Inveraron, Banffshire, Woollen Weaver
James Strachan, 17, Servant, born Dundee, Forfarshire, Woollen Weaver
William McArthur, 15, Servant, born Paisley, Renfrew, Woollen Weaver
Again, I didn't get very far with it, although it would explain why you can't find her birth in Scotland! Let's see if someone else who is not as sleepy as I am can come up with something!
All the best,
Sarah