There is a transportation problem in London, which is so spread out. But soccer flourishes in this city, so it can't be that crucial. And there is a 30-35 minute train from central London to Twickenham, which is in southwest London near Richmond, and not very far south of Heathrow.
London rugby league also suffers from the perception that it is only a "northern game." Richard Lewis understands this, which is why he wants geographical expansion clubs added to Super League. Many parochials in the north, who think only of the prospects of their own club, and want it guaranteed a place in SL, are against geographic expansion.
But the main problem for the Harlequins is that they have no publicity in the major British national newspapers. Most Londoners would have no clue that the Quins are playing on any particular Saturday, no clue that the team even exists. I saw that when I was there a few years ago and the Broncos were playing in the southeast at the ground of major Premiership soccer club Charlton. A local taxi driver, and many other people in the area, had no idea that the London Broncos were playing in the area.
There is also the problem of the saturation publicity of soccer in these same papers. One is bombarded with the game in every paper.
But where the bias / discrimination comes in is where the editors of these papers give massive second place to rugby union, and nothing comparable to rugby league. This is unfair because TV ratings from Sky show that Super League broadcasts are at least 100% more popular than rugby union. The editors are mostly products of private schools where rugby union was the dominant sport.
A change in coverage of rugby league in major national newspapers, including special coverage of Harlequins, would have a huge impact on the crowds at Harlequins, in my opinion.