Even degree characters in principal blocks

We characterise finite groups such that for an odd prime p all the irreducible characters in its principal p-block have odd degree. We show that this situation does not occur in non-abelian simple groups of order divisible by p unless p=7 and the group is M22. As a consequence we deduce that if p≠7 or if M22 is not a composition factor of a group G, then the condition above is equivalent to G/Op′(G) having odd order.