Baker made his first-class debut for Somerset in the 1952 County Championship against Lancashire.
In 1955, Baker made his first-class debut for Oxford University against Yorkshire.
In his five matches he scored 221 runs at an average of 36.83, with a single half-century of 91 not out against Free Foresters.
Baker played an additional first-class match for the Combined Services in 1956 against Glamorgan.
Baker made his debut for Dorset in the 1960 Minor Counties Championship against Berkshire.