Hi Josh
Welcome to the forum, with so little information and so common a name I am assuming a lot here, so don't take what I say as gospel.
There were a lot of William Smith beer retailers in the 1860's but the only one I can find in the Aston area (bearing in mind that Aston was lot larger then than now) is William Smith brewer of the Queens Hotel at the junction of Queens Road and Vicarage Road Aston who also is registered at number 37 Love Lane and 24 Aston Road which I think was a corner property which in fact was the General Wolfe public house. The Queens Hotel with the brewery next door later became Atkinsons brewery.
I have attached a photo of the Queens hotel and the General Wolfe which were both still standing in the 60's but are now gone.