Unexpected Magic by Jude Knight

Jasper Thornton was just a child when his mage-gift first surfaced—a powerful gift that delighted his relatives and won him recognition as heir to the Duke of Findlater.

Twenty years on, he is still failing to live up to that early promise, his power still strong, but erratic and unfocused. Now the despair of his family and of the London College of Mages, he has been reduced to running errands for the duke and the Crown.
Cordelia Nettleford is the ordinary daughter of a couple with only sufficient magic to cling onto the fringes of the peerage. Her parents’ hopes and dreams are fully invested in their only son, her younger brother.

Everything changes when Delia wakes up one morning to find that a dragon has hatched out of a hen’s egg and eaten most of the flock. The following explosion of magical manifestations centered on Nettleford Manor includes the birth of a unicorn. Delia is selected as the unicorn’s maiden.