Going gunmetal grey or just toning this mess? Help

The problem is with grey, even dark grey, you need to get rid of brassy tones as it tends to go browny and murky. I found this out the hard way.

You need to bleach again in my opinion. Bleach London Total Bleach and White Toner should work. I've used so many different lighteners and bleaches over the years and nothing touches Bleach London.

Don't waste money on a white toner, mix your own with a violet dye and white conditioner. If you feel it's more on the orange side of things add some purple-based blue in the mix too. Directions Neon Blue is a popular colour for this.
I can't see the video you linked to so i can't say if your hair is too dark or not. Do not bleach again for at least a few weeks though, hair doesn't heal exactly but does normalise.

It really depends on what shade of grey you want, a pic would be helpful. Do you have they dye already?
You can get a dark grey on a yellow base, but the warmer the base the warmer toned the grey.

EDIT: I've managed to put some pics up!

@capucine: I've made a DIY toner with hot purple from crazy color and that's this pale white/silver on the front of my hair

@Wicked pixie: I only have hot purple right now. I was thinking about waiting for some time before dyeing it silver. Get it to rest a bit. I would dye it purple but I am actively looking for a job so I can't.

i am not sure if the darker yellow might still be too dark but you could try and tone it with pravana silver. It is very blue so it might tone it