The town's WH Smith store will close in June, as will the Post Office. Photo: Google Streetview Birkenhead town centre could keep its Post Office despite plans to shut the WH Smith store in which it is based. The town’s current Post Office, based inside WH Smith, will shut on Saturday, June 5, due to the retailer’s decision to close its Birkenhead store. However, the Post Office said it now has another retailer who may be able to retain the Post Office’s presence in the Wirral town. A spokesperson for the Post Office said: “The operator for Birkenhead Post Office has resigned and the branch is due to close at its current location on Saturday, June 5, 2021. The store where the Post Office is based is closing due to the expiry of the lease.