or we just use larger aircraft to move more people?
That's way too simplistic, there are good reasons that must be understood in order to understand how any commercially viable hub operation needs to work.
Frequency of feed matched to departure waves and handy connections with the right balance between a comfortable connecting time and not hanging around. If you simply operate larger aircraft in a mature market like LHR-Europe Airport, you need to drop prices to fill it and lose yield or drop frequency which undermines your feed.
BA decided to use large aircraft in the 90s when the B734s were banished to LGW and LHR operated with nothing smaller then B757s / B763s on short haul. The coming of the locos killed that idea and BA quickly moved to a similar sized fleet of smaller aircraft in the A320 series.
If you decide to operate to Glasgow four times a day with a B777 you're not going to be making any money....
Even if BA slash frequency to JFK and use A380s on all flights, that'll not dent the problem of a lack of capacity. What larger aircraft do you suggest Emirates use?