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Dig it out an inch deep with a cold chisel, and use a lime mortar (NHL 3.5 for pointing) with a matching colour (I buy from these people).
They sell premix, which takes the guesswork out.
Don't be tempted to use any cement in the mix, or you'll be sacrificing the bricks in the longer-term.
Spray / splash the joints with water first too, or they will suck all of the water out of the mortar, and it will end up sandy and useless.
If in doubt, give the mortar people a call - they love to talk about this stuff.
Can anyone advise of the right mortar mix for pointing this 1896 brickwork? The bricks are soft and fragile but I want to keep them. The existing pointing is a bit more yellow than in photo. It has got damp from run off from window sills - a problem for all the houses on my street.