It's far more usual (but certainly not essential) to place the adverb "concurrently" after the verb it modifies, in the same way as its synonym "simultaneously." :
The building was used concurrently/simultaneously as a public house, possibly from as early as 1825.
The building was concurrently/simultaneously used as a public house, possibly from as early as 1825.
Not much in it really; probably more down to style.
Thank-you so much for your help. I am composing the text for a blue heritage plaque in Runcorn. I have installed fifteen of these plaques already this year, and I am looking to put the next one through on Monday. It will be for The Runcorn Ferry. I wasn't sure which usage was correct because they both sounded a little clumsy, but thank-you for putting me straight.