The English courts may be very willing on principle to give you an anti-suit injunction against someone who sues elsewhere while putting up two fingers to a binding London arbitration clause. But you must play your part and act quickly. You can’t lackadaisically ask the foreign court to decline jurisdiction and then seek to injunct the other guy in London several months later when it’s apparent that it won’t. A hapless shipowner found this out on his unlucky Friday 13. For details see Essar Shipping Ltd v Bank of China Ltd [2015] EWHC 3266 (Comm) (13 November 2015), available on BAILII.
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