I am very familiar with the image of Churchill wearing a French Adrian Helmet. This is exceptional, not a general rule.
The Brodie Helmet was 1st issued to British troops in the trenches in April 1916, and it would not be general issue to front line troops until later in the summer of 1916.
If you are trying to justify wearing either of those helmets for a British soldier living history portrayal in April 1916, during the rising, the photographic and historic evidence really doesn't support it.
"...The O'Brennans, a sept of thieves without any right or title, ... were a perpetual disturbance to the peace of the county,"