The First Speaker, Peter de la Mare, 'spoke for the whole of the Commons' during the "Good Parliament" of 1376, and helped Parliament take a leading role in ridding the Royal administration of its most corrupt elements. This helped the establishment of the official role of Speaker of the House of Commons.
Although this happened during the Hundred Years War, this was not the direct cause of Parliament's intervention.
Edward III was old and senile, his eldest son, the Black Prince, dying of dropsy, and the heir to the throne thus the 9 year old Richard, son of the Black Prince. This made it likely that a minor would succeed to the throne, the corrupt royal uncles then being the real power in the land.
Hence, the intervention by Parliament in a time of crisis
So, although Parliament took a significant part in purging what were seen as corrupt elements in the royal administration in 1376, this was an unusual situation and didn't last.In the "Bad Parliament" of 1377, John of Gaunt imposed his own choice as Speaker, and in future the Crown almost always got its own way in the appointment of Speaker for each Parliament.
Thus, the Hundred Years War didn't help Parliament gain more power over the king, although the position of Speaker of the House of Commons was first established in 1376, this was really unconnected as such with the war, having more to do with who would hold real power during the minority of the future Richard II.
