Final answer:
Basophils are the type of white blood cells that contain granules with histamine and are responsible for allergic responses by dilating blood vessels and increasing their permeability.
Step-by-step explanation:
The white blood cells that contain granules with histamine are called basophils. Basophils are a type of granular leukocyte and are the least numerous of all white blood cells. They secrete histamines, which are responsible for dilating blood vessels and increasing their permeability during inflammation. Additionally, basophils release heparin, which inhibits blood clotting and aids the movement of leukocytes into areas of infection. While eosinophils also play a role in allergic reactions and release anti-inflammatory compounds, they primarily target parasitic infections.