Wakefield trailed 42-6 until the 65th minute before a late rally got them to within eight points of the hosts.
However, it proved too little too late for Chester's side as they suffered a bout of déjà vu in the capital.
Trinity were beaten 42-24 in London in round one and produced another poor display which saw them slip from third to sixth in a congested Super League table.
"They were 13 from 13 and we were 4 from 10, it was exactly where we left off last weekend against Widnes" said Chester of his side's early completion rate.
"Our ball control was woeful, we had too many guys today that didn't want to get on the ground and too many guys that wanted to take shortcuts in terms of the third man in the tackle.
"We got burned by a much better team.
"They are scrapping for survival and you could see that in the first 60 minutes.
"It is just appalling; the effort from some individuals, and collectively we have just got to take it on the chin.
"I take responsibility for the changes we made but I won't take responsibility for some of the desire and the effort levels that some individuals had out there."
He added: "I feel sorry for the people that turned up to watch that. I don't want to take anything away from London Broncos, they were very good but we were woeful."
Jordan Abdull was the star for the Broncos as he crossed four times in the first half to help give his side a 26-6 interval lead.
Rhys Williams grabbed London's other try in a dominant first period while Kyle Wood kept Trinity in touch with a score under the posts.
Williams scored a second after the interval while Kieran Dixon crossed twice to put London 36 points ahead.
Trinity fought back with doubles from Dave Fifita and Mason Caton-Brown, along with one try from Ryan Hampshire.
However, there wasn't enough time to complete a comeback as Wakefield left London empty handed for the second time this year.
London Broncos: Walker; Dixon, Morgan, Kear, Williams; Abdull, Smith; Battye, Cunningham, Butler, Pitts, Lovell, Yates. Subs: Pelissier, Richards, Gee, Adebiyi.
Wakefield Trinity: Hampshire; Jones-Bishop, Lyne, Sa'u, Caton-Brown; Reynolds, Miller; Fifita, Randell, Hirst, Batchelor, Horo, Crowther. Subs: Kirmond, Kopczak, King, Wood.
Referee: Liam Moore (RFL)