Antonin Boullemier was born in France and studied ceramic painting at several ceramic establishments. He apprenticed at the Sevres National Porcelain Factory before moving to England to work for Minton's. He specialized in painting cherubs.
Interest in older china has fallen off and antique dealers claim they are hard to sell. I imagine the auction house could not give you an estimate because they have no way of knowing if there would be interest in your Minton china at an auction.
You can have an appraisal done at Kovels or Replacements. They will show the retail price of your china. If you want to sell it to them you will earn far less than the retail value but that can be said about any other seller whether an auction house, antique dealer, or consignment shop.
You can learn more about your china if you check out the Minton site (Minton Archive).