I can answer some
why do most flights get to LHR via Lambourne when most of the world is not to the north-east?
Traffic doesn't just route via LAM from the North East. Anything coming from the east of Heathrow tends to come in via LAM. (Holland, Belgium, Germany, eastern block, Russia, Scandinavian countries, the far east etc). BIG traffic tends to come in from parts of France/Spain, Italy, Africa and other countries to the south east. OCK traffic tends to come from over the pond, parts of France/Spain, South America. BNN traffic tends to come from across the pond and UK domestic destinations.
why are there days (with decent weather) when all the stacks are full for hours on end and other days when holding is the exception?
There are lots of factors. Could be due to weather, airline schedules, atc staffing, the list is endless.
why do some US/Canada/Dublin flights arrive via Ockham?
Over the atlantic ocean are a series of tracks, called NAT tracks. As there is no radar over the ocean, aircraft must fly on these prescribed tracks at certain altitudes, several minutes apart. The tracks tend to be aligned with the wind. If the jet stream is further north, the tracks are northerly (so the planes have the wind behind them when coming east bound). if the jet stream is to the south, the tracks are southerly. So when tracks are northerly, aircraft tend to come in over scotland and down the UK into BNN, and when they are southerly, aircraft tend to come in over Wales and the South west into OCK.
why would two consecutive flights to Singapore turn right and left on leaving LHR?
Depends on the route that they have planned to fly. There can be lots of different routes to get to the same place. Airlines will plan on the best route for that aircraft on that particular day, taking into account lots of factors such as weather conditions, fuel required, aircraft weight etc. The aircraft turning right off 27s (left off 09s) is leaving UK airspace via Clacton, the aircraft turning left off 27s (right off 09s) is leaving UK airspace via Dover.
how much disruption is caused by the 1500 runway swap, and how much when the runway changes from 09 to 27 or vv?
From a radar point of view, switching from 27L to 27R or vice versa causes very little disruption, if any. The only complicated bit is working out which aircraft is last/first on either runway. When switching from 09 to 27 or vice versa, things can get very complicated. I don't know what disruption is caused on the ground, I'm not a tower controller. Someone else will have to answer that.
Why do aircraft fly Biggin-Epsom-almost back to Biggin before lining up with the runway? It makes for a lot of unnecessary noise and pollution over London and I've have thought the purpose could be served just as well by flying out east until it's time to turn onto the approach.
It's all to do with the set up of the airspace. Heathrow isn't the only airport in London.
Do aircraft flying to say Farnborough or Biggin Hill have a sort of dedicated tunnel to fly through, or are they directed to avoid whatever other traffic is around at the time?
They fly on prescribed routes, which keep clear of other airports traffic (to a degree!)
Most Detling departures fly past Biggin at < 8000', but a few are well clear at 10-12000'. Couldn't they all get that high to avoid inbound traffic?
Unfortunately not. All aircraft climb at different rates. We have to ensure that planes are kept either 3 miles or 1000ft apart. A lot of the time, there just isn't the room to get them going up and away from the inbound aircraft, so they are stuck low down.
I'm sure others will chip in with ones I've missed, or to add more content
