It is illegal to sell a horse without a passport. Registration and passport applications normally to hand in hand. If your situation is complicated contact the Horse Passport Team at DEFRA.
The keeper of a foal is responsible to see that a foal has a passport and is microchipped at the latest within six months of birth to allow for foals born in October say. The owner may be the keeper but if you bought a foal on the mare to be delivered on weaning you may be the owner and should apply for the passport but the keeper is the person who is mainly responsible under the 2008 Horse Passport Order. If the mare and foal have pedigrees make sure you use the best studbook not an ID passport issuer.