Phyllis Briggs wrote several animal stories for children, as well as three pony stories.  By far the best known of these is her sequel to Black Beauty.   As astute readers of Anna Sewell’s Black Beauty will know, Black Beauty was a gelding, and hence was never going to have had a son.  My copy of Son of Black Beauty does acknowledge this fundamental objection to the whole premise of the book thus: “in this book the art of the storyoteller has been enlisted to produce what Black Beauty the horse could not - a son.”  

The Pickles books are both early readers.

Finding the book:  very easy to find indeed in all its incarnations.

Links and sources:

Phyllis Briggs

Son of Black Beauty

Thames Publishing Co, London, 1952, Regent Classics Series,
256 pp.

Dean’s Classics no 42, 1973 (abridged), 184 pp.

Dean 1978, 44 pp.  Retold and illustrated by Georgina Hargreaves

Bibliography - pony books only

Pickles the Pony
Juvenile Productions Ltd, London, 1959, illus G Higham, 61 pp.

More Stories of Pickles the Pony

Juvenile Productions Ltd, London, 1959, illus G Higham, 61 pp.

ALSO:

Horses and Ponies of the World Picture Stamp Book

Purnell, London, 1966