The answer is yes - and no.

Speenhamland is an area within the historic parish of Speen - part of Speen but not the same as Speen. Speen is the parish that lay on the northern boundary of Newbury. Speenhamland is/was a tithing or hamlet of Speen and was a manorial holding in its own right by the later middle ages. It was the most economically successful part of Speen, taking advantage of its position on the main London to Bristol/Bath road where it met the north/south route between the Midlands/Oxford and Winchester/Southampton.
Newbury started south of the River Kennet but grew north along the north/south road and soon met Speenhamland. By Tudor times Speenhamland was part of the town of Newbury but not the Borough of Newbury. In 1878 the Borough boundaries were expanded to incorporate Speenhamland and other parts of Speen and Greenham.