Transport Blog has a discussion of the weird, regulated world of airport landing fees and suggests that there must be some pretty weird incentives in place, without actually knowing what they are. Because I am a sad geek, I have investigated the matter at length, with the following conclusions

Okay, let's have a go.

Business travellers out of London prefer to use Heathrow, mainly because there is a greater choice of flights and connections. On routes where there are significant numbers of business travellers and there are existing flights out of Heathrow, it is virtually impossible for new entrants to the market to compete by flying to the same destination out of Gatwick or Stansted, even if the total demand for seats to that destination is increasing. This because the business class travellers continue to go to Heathrow, and it is virtually impossible for a full service airline to make money with a plane full of discounted economy passengers. As demand goes up, the existing Heathrow based carriers simply increase the proportion of business class seats in their planes and make monopoly profits, and the total number of economy seats on the route drops. This is perverse, but if competitors introduce flights from Gatwick, they are still unable to make money as the premium traffic remains at Heathrow, and they pick up only economy passengers. (It is very difficult to compete for the business traffic on price, because travellers are generally not paying for their own tickets).

Ideally what you would like is for competitors to be able to fly from Heathrow also. That way, business traffic would be split between the carriers, the existing carriers would have their margins eroded, the new carrier would be able to make money, and we have two carriers making normal profits rather than one making monopoly profits and the other losses.

Why does this not happen? Generally, new carriers are not able to fly from Heathrow, because of a mixture of outright protectionism (eg the Bermuda II treaty that restricts the UK-US market to BA, Virgin, United and American) and a shortage of slots. However, this shortage of slots is a consequence of the regulatory situation, not anything innate.

There are lots of carriers flying on small, insignificant routes, that none the less have rights to fly from Heathrow. (Normally these are national carriers of insignificant countries that gained these rights many years ago and have had them grandfathered in). In most cases, it doesn't matter if these airlines fly from Heathrow or Gatwick, because their passengers have no choice of airline and they will fly from whatever airport the flight goes from. Ideally you would want these airlines to move to Gatwick or Stansted and make way for airlines flying on more competitive and economically more important routes. There are two ways you can do this. You can increase landing charges at Heathrow (ideally to what the market will bear) but not at Gatwick, and give the smaller airlines an economic incentive to move. Alternately, you can simply allow these airlines to sell their landing slots to other airlines for large one-off payments. Neither of these things are presently permissable, and as a consequence we have a less competitive aviation market than we should. This means less choice of flights for passengers and higher fares.