Right CherryDrops
Red tones are hard to get rid of, (unless you want to keep them, in which case they seem to wash out in the shower, bleed onto your pillowcase, and fade to pink in days!) - they always seem to peek through under lights.
You need to be a bit careful about layering on yet more colour or you will just go muddy and you will still have red tones in sunlight! They are there, they aren't really going anywhere.
You have 2 options. You strip the colour out, using ColourB4 Extra Strength, cover the hair that will be revealed which is likely to be gingery with a Nice n Easy Medium Brown or Light Brown 8 wash as you cant use semi or permenant on it (containing peroxide) for 1 week due to reoxidiation, and it will look a bit shit for a week but not too bad, then do a permenant colour in your chosen colour (with ash, because the revealed hair will be a bit gingery). This is the best option as you will be getting rid of "build up" and starting pretty much from scratch, and toning your hair rather than doing a complete colour change.
The 2nd option is that you go to a salon and get a full head of highlights (or maybe a half head will do) and then cover over the lot with something neutralish (dont use anything too ashy over highlights though you might get away with a dark ash blonde) so neutrally colour, maybe Loreal Recital Preferance Rimini (though to be honest, if you have the money to get highlights, get your hairdresser to tone them with an ash to kill out the gold a bit)
Personally I would do the ColourB4, in fact I have done it, I got rid of MEGA red tones (see the pictures on my profile) - left me with a pinky ginger, coloured over that with Nice n Easy 114 Light Ash Brown, a few weeks later I had a full head of bleach highlights which left me with a Jennifer Annistony look (I think some of the ash brown had washed out in the meantime, revealing a toned down version of the ginger, if that makes sense)
After that I did my roots with Loreal Rimini which brought my light to medium brown (with gold cast) natural hair up to a very light golden brown (but you might be different, we would need to reassess your new "root" colour if you did this)...