Give notice and give a date. Four to six weeks is enough for a client to plan around and short enough that it does not hang over the whole book. Tell people in the chair first, then in a message to everybody else, then change the prices on the day you said.
Say it in one line and do not justify it at length. 'From the first of March my colour prices go up by ten pounds. Your next appointment on the fourth is at the current price.' The longer the explanation, the more it reads as an invitation to negotiate.
Honour bookings already made at the price they were made. It costs you little, it removes the only genuinely unfair-feeling part of an increase, and it gives your regulars a reason to book ahead immediately, which is worth having.
Expect to lose a few clients. That is what an increase does, and a small number leaving is not evidence you got it wrong — the arithmetic that matters is whether the remaining book at the higher price beats the whole book at the old one. Usually it does, at a much lower cost in hours.
Raise a little and regularly rather than a lot and rarely. Annual single-digit increases barely register; a thirty per cent correction after four years of standing still is the one that empties a column.