Sounds like yours is an example of how renting can be a success for all concerned.
With regard to your question about buying, I would say go for it, but suspect it will depend on your landlords circumstances regarding that property, are they professional landlords,is it mortgaged, are they waiting to sell upon retirement etc.
Personally I would look at any offers for mine and would probably be happy that a tenant feels that way about it, but ultimately it would have to suit in a financial way.
I may have read somewher about a proposed discount scheme for tenants buying(like they did in council houses) but cant see how they could force it in the private sector, but good luck and hope it comes off. Maybe you could keep us posted in this thread.