Something that should be pointed out (as it is always, always forgotten) is that when there is a sizeable swing, it tends to be a lot higher in marginal seats, thus it's always easier to win a majority than a uniform swing suggests.
No, that's not strictly true. Swings in socially polarised marginals can often be relatively low (this contrasts with low turnout elections of course, where swings in socially polarised wards or constituencies are typically unusually high). It's more that swings tend to be highest where there are big concentrations of swing voters.
Swings tend to be greatest in "medium marginals" aka the seats needing 4 - 10 point swings to change. The really close seats that need like a .4% swing will always be incredibly close because the incumbents realize how much danger they are in and work their asses off. Its the Labour MP who won by 12 last time, but who sits in a seat the Tories held for decades prior to 1997 that is going to have to really worry.