Finding Western engines for the MiG-29K and Su-33

What Western engines could replace the MiG-29K's RD-33MK and the Su-33's AL-31F in a Westernized carrier-aircraft scenario?

The panel cannot identify a direct British replacement; an RB199-related option is tentatively raised before the answer settles on asking Rolls-Royce for a bespoke solution.

The answer depends on whether the imagined conversion belongs around 1976 or much later, alongside Vikramaditya's Indian service. The date remains unsettled as the panel works through the scenario. An RB199-related possibility is tentatively suggested for the earlier period, but nobody identifies a suitable direct British replacement for either Russian engine. The practical suggestion is to ask Rolls-Royce to develop something specifically for the requirement. This remains a tentative response with acknowledged limits of expertise.