Heathrow capacity

Just a quick question which I am sure someone will help me with please:-

Clearly slots are allocated, they are like goldust and airlines cant just operate more flights at will. However, are there any restrictions on the size of a/c used. EK had 5 pairs of slots which they now use for 5 x 380 daily to DXB. Would they have needed permission as this will generate a lot more pax than say 5 x 777?

Is the answer to the capacity issue to use bigger planes, less frequent to some destinations allowing slots for new services? Guess there is some restreiction as I know only limited gates can host 380's, but am I being to simplistic???

Many thanks

Different aircraft need different separation distances on approach/takeoff due to the amount of wake turbulence that they leave behind them - most widebodies are known as 'heavy' aircraft - but the A380 is in a class of its own known as 'large' meaning that there's greater distance needed behind them.

How this relates to what a/c can be used for a particular slot I'm not sure but imagine it'd have some sort of impact?