Anothertyke is absolutely right. Competition would better be provided by expanding LHR, where the current barriers to entry result in the incumbents having market power. Expanding LGW wouldn't help resolve this. The imbalance between demand and capacity at LHR hasn't been resolved by the fact that the other London airports have had substantial surplus capacity for years. And it wouldn't be resolved by a second runway at Gatwick.
It's worth reading easyJet's submission to the Davies commission.