My son was a lot like this.I t's frustrating for you, but not the end of the world. He is only just a year old, and to be honest, children of this age are only just starting to reach the stage where they need more nutrition than milk can offer.
Does he still have milk in a bottle? Perhaps it's time to move him on to a cup so that he is only drinking milk when he is genuinely thirsty, rather than drinking for comfort and then getting too full to eat.
Perhaps you could also try him with soft, milky meals - yoghurt, rice pudding, milky ready brek/fine milled porridge, other milky puddings - to ease his transition on to proper solids?
Some people will advise the opposite, but I say - if you can find some foods, especially finger foods, that he really likes, let him eat that every day if he wants, just to get him used to eating solids.
If it's any consolation my son hardly ate a thing until he was about 2 yrs old and it's only since his third birthday that his appetite has become much bigger. He has always been perfectly healthy and strong.