This biography is available online and it makes sense to me.They couldn't have children until she was accepted by his family, or maybe because they didn't have money to start a family. Anyway, maybe that civil document or the passenger lists can be found.
https://gemology.se/gill-library/gemjewelry/Barnato_Barney_ie_Barnett_Isaacs_1852-1897_a_Memoir_Harry_Raymond_1898.pdf"After breakfast I walked down to the club with him, and
his mind was still full of the children.
'Isn't it strange,; he said,
Fanny and I were married for eighteen years and no children,
and now we have' Miss Barnato' and Jack, and we must get back to London at once."
"Barnato was most fondly attached to his wife and children,
and they accompanied him in all his journeys to and from
London. In the earlier days, before the children came,
Mrs. Barnato accompanied her husband on his journeys to the
Hand and Capetown, when the only conveyance was for the
richest a cart or special coach, over rude trackways that an
English coachman would despair of."
"Barnato met his future wife at Kimberley in 1874, and in
1875 they were secretly married by the civil law. The
marriage was kept secret for some time, for Mrs. Barnato was
not of the Hebrews, and the marriage was certain to be
bitterly opposed by his family. However, Barnato had taken
his own way, as he generally did; he married the wife of his
choice, a most able, accomplished and clever woman, and the
family objections were overcome when Mrs. Barnato adopted
the Hebrew faith. The children have, of course, been brought
up in that faith.
The eldest child, the daughter named Leah Primrose, after
Bamato's mother and his first Transvaal mining venture, was
bom at 28 Park Lane on March 16, 1893.
The next child, a boy, named Isaac Henry Woolf, was born
at 36 Curzon Street, Mayfair, on June 7, 1894. He is
commonly called Jack, and is the hero of the bicycle.
The third and youngest child, a boy, named Woolf Joel,
was bom at Spencer House, St. James's Place, on September 27, 1895."
