from blonde to brown back to blonde!! HELPPP!!

 

2 weeks ago I went from light blonde hair to light brown, but in order to not turn my hair green my hairdresser put in red to add warmth!! but now my brown colour has faded and I'm wanting to go back blonde (without bleach) but my hair has too much warmth in it so putting any light colours on would just turn it brassy/ginger so I'm wondering how to tone down the auburny warmth colour before I start lightening it? would a dark ash blonde tone it down? its fading really quick thankfully but can't rid of the warmth :(

any suggestions most welcome thanks a lot peeps!!