No, John Palmer lived or worked in Coleman Street itself from around 1770 to 1789. I've found him listed in directories as an an attorney in Coleman Street. My ancestor (and other possible children) was baptized in St Stephen Coleman Street.
From 1789 until 1797 he was listed in Lyme Regis land tax records.
I think his brother described him as such to prove he was the same man as the one who wrote the will. The will was written back in 1771 when he was living in Coleman Street.