I have found that the various discount ticket places in the main actually only really sell cheap seats at cheap prices (ie you are really paying full whack).
The ones that abound near the theatres, and in tourist areas, actually just sell the cheap seats witha mark-up. Avoid them like the plague.
As in NY I have found that in London that generally you get the best still available seats at the best prices by going into the theatre itself to book and ask what is available.
However for new shows that are sold out, or near too it, that does not work in terms of getting reduced prices and so for certainty and trip planning buying in advance online is probably best. However London has so many, many shows on that is rarely a problem.
Last time in London we gorged on 6 shows in 5 days.
Matinees often allow a better selection of seats and/or reduced prices.