The Broncos, who had acquitted themselves admirably for an hour, were swept aside after that by an irresistible tidal wave of six tries in 20 minutes - and that's after they had been given a 10-point start.
With traditional Wembley weather to mark the last final at the stadium, stamina was going to be an issue. London came out to face that test led by Peter Gill, their captain, Shaun Edwards, insisting on him having that honour whilst he brought up the rear, his heavily strapped thumb gleaming in the sunlight.
Within a minute of starting the serious business, McDermott was driving into the London defence and Terry Newton was bursting through from dummy half to be stopped on the line by Tulsen Tollett. It was a crucial tackle, after Leeds had made ground with such ease and it looked even more significant after five minutes when London seized the lead.
Karle Hammond moved the ball to the left and John Timu's kick flicked off Richie Blackmore's heel to sit up perfectly for Martin Offiah, who knows his way to the Wembley try line.
The vestiges of his legendary pace left him with just Iestyn Harris to beat and he cut inside him for a try which Rob Smyth converted from wide out.
It was now a test of Leeds' equilibrium and it was found wanting when Marc Glanville, not watching play, allowed a pass to bounce off his head. From that surrender of possession, London attacked again and Hammond's pass missed out Greg Fleming who nevertheless attracted the tackle to allow Robbie Simpson a clear run to the line. Smyth could not add the two points but a lead of 10 was beyond any London followers' wildest dreams.
Leeds began to exert some pressure when Harris's clever kick saw Offiah tackled in goal and their first point came when Edwards was harshly adjudged to have tackled Ryan Sheridan high, Harris putting over the simple penalty point. The hot favourites were still in trouble and could have been in more if Sheridan had not got back to beat Hammond to a kick through. Having escaped the prospect of conceding a third try they came back into the game, thanks to the veteran stand-off Daryl Powell, who dummied his way across the London defence and then accelerated through a gap to lob a pass out to Rivett. Although Offiah seemed to get his fingertips to the ball, the Rhinos winger was able to gather it and score.
Harris's missed conversion and a try from Darren Fleary that was disallowed for obstruction left Leeds still trailing by four points as half-time approached but growing stronger.
Two minutes into injury time they finally repaired the early damage and took the lead for the first time. Fleary, who had a superb half, again broke the Broncos line, Brad Godden supporting and exchanging passes with Lee Jackson before plunging over, Harris putting them in front with his conversion.
London were not quite ready to fold two minutes after the interval, Hammond did magnificently to get his pass away and Matt Toshack's speculative kick bounced kindly for Fleming to surge past Francis Cummins and score.
A penalty for Timu's marginally late tackle on Rivett led to Leeds retaking the lead, McDermott thundering through for a classic prop forward's four points, transformed into six by Harris's boots.
Leeds finally broke the Broncos resistance with two marvellous tries in two minutes. Sheridan began the game's decisive train of events with a wonderful break from the scrum base. Although he was caught by Smyth, a long pass from Harris gave the winger room to score his second.
Adrian Morley then strode through only to be stopped by another brave Tollett tackle. Again it was courageous defensive work performed in vain, Andy Hay and Jackson sending Marcus St Hilaire over and Harris again converting.
Rivett then became the second player after Robbie Paul in 1996 to score a hat-trick at a Wembley final, intercepting from Hammond to go 90 yards and Leeds equalled the 40 points St Helens saw that year when St Hilaire put Harris over.
The new record arrived as London, dead on their feet, watched Cummins flash past them on the left wing and, in the last minute of normal time, Rivett danced in for his fourth, Harris's eighth goal also giving him a share of the record for a player at Wembley.
Leeds Rhinos: Harris, Rivett, Blackmore, Godden, Cummins, Powell, Sheridan; McDermott, Newton, Fleary, Morley, Farrell, Glanville. Substitutes: St Hilaire, Jackson, Hay, Mathiou.
London Broncos: Tollett, Smyth, Fleming, Timu, Offiah, Hammond, Edwards; Retchless, Beazley, Salter, Millard, Simpson, Gill. Substitutes: Toshack, Callaway, Ryan, Air.
Referee: R Smith (Castleford).Reuse content