Been anaemic for 5 years. Seen a haematologist for 4 years. Get regular iron infusions. Told I don't absorb iron orally. What could cause this?

Many things. Iron absorption requires a healthy stomach that produces stomach acid and a healthy duodenum to absorb the iron. Also, iron loss can be occuring (menses, GI blood loss, etc.) and if you absorb iron, but not enough to match what you are losing, you will be deficient. The most common malabsorption problems are celiac disease and gastric bypass, but there are other causes too.