You can remove colour build up with a product called ColourB4. If its dark colours that have built up I'd recommend the Extra Strength.
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You then have to wait a week to colour (I know! But its worth it)
After that, I suggest you move to professional dye if you are very grey. Loreal Majirel is the best for covering grey, 5.3 mixed in a 3:4 ratio with 6.0 as your base, with 20 volume developer. 1 and a half times developer to colour ratio.
So 2 teaspoons of 6.0, 6 teaspoons of 5.3 and 60ml of 20 volume developer makes 100ml and should cover a full head.
Read all the links from this webpage to make more sense of all that.
Products available from this website or eBay.
If all that sounds scary, go to your hairdresser, tell her you want a colour cleans and colour correction, she will sort your base shade out, you can then maintain it at home using the combination mentioned above (but only do your roots - buy a tinting brush or even a foundation brush and only paint it on the bits that are new. Get your DP or a girlfriend to help you do the back. You can always get it done professionally twice a year or something but maintaining 3 weeks of grey etc it will be fine)
The mix I mentioned above is a "deep basic" mixed with a "colour". The deep basic is dark blonde and the colour is light gold brown, mixed together in that ratio they will give you a nice warm slightly golden brown with the full range of natural tones to "fill in" what is lost by the grey hair but not too dark and there is absolutly no red in that either. To avoid red tones, never use a dye (box or otherwise) that has a number 5 or a number 6 or even a number 4 after the main number. So 5.4 would be light copper brown. 4.45 would be a medium copper mahogany brown. The main number relates to deepness, so if you don't want to go too dark, never use anything where the first number is lower than a 5. 5 is light brown, 6 is dark blonde, etc.