Hi Chilli Pepper,
A very warm welcome to Rootschat.
I think the best starting point would be to find him in the 1911 census index.
www.1911census.co.uk. I think he and Jane may be living in the district of North Brierley.

One possible birth registration would be the one registered in Hunslet:
James Henry Harrison, Hunslet, Sept Qtr. 1876 volume 9b page 320.
You could try putting Hunslet for his place of birth in the 1911 census

What was James Henry`s occupation on his marriage certificate?
Regards,
Mo