Little scope to expand my HR role in small charity

I work for a small third sector organisation, which last year paid for my level 3 Foundation course, and am now a Foundation member. 

As the organisation is around 16 people from the CEO down there is, on the surface, very little scope to expand into a HR role from my current (Research Assistant). I have seen elsewhere that getting into a HR role is very competitive and I don't feel like I have the HR skills on my CV to actually move into the sector. 

Do I play on my transferable skills and interest of law/policy and/or ask to take on some of the HR at my current org. to build a practical base? 

I would be interested to hear opinions on what hiring managers would be looking most for and from those who have entered HR from another field

Thank you. 

Holly