Going from blue to brown without bleach?

I'm not an expert at any of this but I have experience using Adore colours and I'm sure one of them would cover up your hair quite well!  The darkest one I've used on my hair so far was copper brown, unlike the name it is more of a purpley brown and it seemed to have strong coverage.    There are quite a few dark browns in the Adore line, so maybe you could order a few different colours and experiment?  If you haven't used Adore they are good for your hair, not damaging at all and even though they are semi-permanent they hold colour really well. 
As I said I'm not an expert at any of this at all, but I'd think a warm brown would help counteract the blue.  If I'm wrong I'm sure someone will hop on board and correct me!!!

Thank you!  🙂

I like to neutralise bright colours with their opposite shade when going back to natural. So put a red/orange over the blue green first, the resulting sludgey brown will be easier to cover with your chosen shade.

How about trying a colour remover, I've read on here you can use them upto 3 times?? Then you know why base you're dealing with and can put a semi over?

Orange is opposite blue, and red is opposite green on the colour wheel so technically putting an orange over the top first (like Stingle said) should give a better base for the brown to cover. In this picture your hair looks mostly green so applying a reddy based brown would also work