[Tahti]

Special Effects dye is very good, long lasting and pigmented. I used to dye my (non bleached, ginger) hair pink with Stargazer magenta, that was good too.
Unfortunately for very bright unnatural colours, you're not going to get a great effect unless you bleach - you will get colour, but it will fade out very, very quickly.

True blue dye will absolutely NOT show up properly on any hair that isn't bleached, or blonde - dying it over red toned hair will just create a murky brownish effect. I used to have blue hair and I had to bleach it out a lot to get the colour right, because any leftover yellow will make the blue dye look green.

Red is easier to come by though, and can be dyed over hair - for a pillarbox colour red however, you would have to bleach... unless you bleach your hair you won't be able to get truly bright colour. (I'm speaking from experience of 3+ years of dying my hair unnatural colours)

Here's a site that sells SFX dye - BU special effects manic panic pink hair dye accessories

Hope you find something that works!