1. How do you know that the John White in Barrow is the person you are looking for? Both John and White are fairly common names, and Ernest is not that uncommon.
2. Have you looked in the births registry? In the quarter ending December 1900 (just because he was born in September doesn't mean that was when the birth was registered - and the BMD's go by when an event was registered, not when it occured) there are eight plain John Whites and 21 John and a middle name White. Similar numbers on the quarter ending September.
3. Having looked on the 1901 census there is a Mary J White on the line above Ernest White. Would this not be his wife?
4. Where was John married, and where were James Macrell and Co based. If these were in Barrow then there is a chance that you have found the right person. However this is no guarantee, as I have found with my family. My Gt Grandfather came from Newcastle-Upon-Tyne but married my Gt-Grandmother in Kirkby Lonsdale.