According to the MTA's report congestion will actually increase in the Bronx especially the Cross-Bronx Expressway. So we are just shifting traffic from the 'CBD' of Manhattan to the less affluent outer boroughs. Manhattan below 60th street is majority white and has a median income of $83,008, the Bronx which is around 90% non-white and has a per capita income of $23,862, seems like they want to shift traffic from white areas to non-white neighborhoods. Also I don't know how this will affect traffic flow in Manhattan, delivery trucks will continue to clog Manhattan streets unless everyone gets a cargo bike and taxis/ubers are still needed in Manhattan and will also clog streets. NYCDOT is on a mission to make driving in Manhattan worse and worse and this congestion pricing further drives that mission but trucks and taxis aren't going away anytime soon regardless of what politicians and new urbanists want.
Also a couple of things, the London congestion pricing is only in effect from 7 am to 6 PM M-F and from noon-6 PM on Saturday/sunday and covers a much smaller geographical area, NYC congestion pricing is 24/7 including weekends from my understanding.