This is because of the decreasing electronegativity. Alkali metals tend to lose electron and attain the noble gas configuration. The halogens, on the other hand accepts electron to gain the noble gas configuration. This electron accepting tendency decreases with decreasing electronegativity.
So when halogens and alkali metals react, the electron given out by the alkali metals is accepted by the halogens. So, the reactivity depends on how effectively that electron is accepted by the halogens. Since, the electronegativity decreases from fluorine to iodine, so does the reactivity.