A few reasons. The main one is that the club hasn't ever had a proper home stadium, drifting between different soccer and RU grounds every few seasons which most of the time were in completely different parts of the city, meaning that putting down foundations in any one area was impossible. Because of the size of the place, people from London tend to associate themselves with the district or suburb that they're from rather than 'London' as a whole, and traveling from one side of London to the other can take as long as traveling between Hull and Warrington (the two geographically furthest Super League clubs in the North), so trying to market a club in an unknown sport to the whole of London is spreading resources way too thinly, it just gets lost in the ether.
Also they've been really badly run for most of their existence by people who either didn't understand the task they were facing or had their hands tied. Most of the time as London Broncos in the early days of Super League was spent trying to make the whole thing 'Aussie-themed' in an attempt to appeal to ex-pats living in London, which was a stupid approach because these people are no more likely to become RL fans than anyone else, they are only in the area for a limited amount of time before moving on and if they are RL fans then they're likely to attend the matches anyway. More recently the club was marketed as 'Harlequins RL' as an offshoot of the RU club, which obviously wasn't ever going to work and saw them lose a lot of the support that they had. Now they're the Broncos again but with no real identity, and all the while moving between various stadiums throughout the city. There's actually a huge amount of youth development in London, I'd guess a lot more than in Melbourne, but the Broncos don't ever benefit in terms of supporters because they don't actually appeal to any one group of people.