Why the Royal Navy did not need its own Ulithi

Did the Royal Navy establish an Ulithi-like forward base of its own?

Not in the same form; it could use Ulithi when needed and instead relied on forward support from Australia and the Indian Ocean.

British forces could use Ulithi when needed. Their forward support also drew on Australia and the Indian Ocean, whereas American forces were advancing across the Pacific from the opposite direction. Those different approaches affected where each navy needed its support facilities. The Royal Navy consequently did not build an equivalent island base in quite the same form.