I think it depends if he (sire) is registered with British or Irish society. I found out about my boy's breeding on Connemara Pony Breeders Society website - www.cpbs.ie - but there is a British one too - www.britishconnemaras.co.uk
Hope this helps!
Oops, I gave you the total wrong website the other day, sorry! Here's the site I found info about mine on: www.connemara-pony.com
I can't see Lays or Leys Conker on there, but there are two other Leys ponies. Also a few apples but not your one. But if you look at the pedigrees of the other Apples and Leys you might find a connection to yours, or find details of the breeder of them and be able to contact them directly.
Hope this helps more than my previous useless post!