South African independence and British sea power in 1914

Would Britain invade if South Africa declared independence in 1914?

Not for independence alone, but a pro-German South Africa would likely face a severe British blockade and would lack a navy able to contest it.

South Africa became a self-governing dominion in 1910, gaining control of domestic affairs while Britain retained responsibility for foreign relations. Britain would not normally invade a dominion simply for declaring independence. The strategic calculation changes if the new state supports Germany. South Africa had not developed a navy under dominion status, so it would be vulnerable to British maritime isolation. A blockade would be more likely than an immediate land invasion.