Following the club's 29-20 victory in Wednesday night's second-leg encounter, the club now need another significant victory off the pitch if they are to claim a place among England's elite clubs next season.
London Welsh have outlined their determination to appeal the decision - made by the Professional Game Board and approved by the Rugby Football Union - to block their promotion.
Chairman Bleddyn Phillips vowed before the game that London Welsh, if crowned champions, would do "everything within our power" to overturn the RFU's decision.
London Welsh came into the second leg of the play-off final at Oxford's Kassam Stadium - their proposed Premiership home - with a 16-point advantage.
They overcame a spirited Pirates performance to seal victory on the night with tries from Hudson Tonga'hui and Jack Moates and 19 points from the boot of full-back Alex Davies.
The Pirates had threatened a comeback when wing Matt Evans finished an electric breakaway try to put them 13-6 ahead.
But by the time Ryan Storer drove over for a try five minutes from time, the Championship title was already heading to Old Deer Park.
The result will extend the uncertainty for Newcastle, who finished bottom of the Premiership but do not yet know whether they will be relegated.
"Hopefully everything off the pitch will get sorted now. We have given the RFU something to think about," London Welsh captain Jonathan Mills told Sky Sports 1.
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