Having spend a fair bit of time being paid (by NATS) to watch arrivals at Heathrow about 20 years ago that's a seriously long lens. I used 8-12x binoculars to get an earlier chance to ID types on arrival and you wouldn't get a view like that even with 12x. Without knowing the weather conditions on the day, but assuming they're typical, you can tell from the haze that the planes are far apart - look how much less sharp each one is than the one in front of it (the 5th is recognisable as an aircraft but only just). I suggest that the later twins are larger than the one at the front, further shortening the appearance, thus they're all further away than they look. This would also explain why the last doesn't have its landing lights on.
Adding up the wake vortex separation (relevant tables) as an estimate of the length of the shot and assuming we have a Medium (seperation not dictated by wake vortex so I've used a low figure of 2.5 NM) followed by 4 Heavies (4 NM required for a Heavy following a Heavy) we have 14.5 NM from the first to the last. With no ground in sight we can assume that the A320ish is still some way from the threshold, so it's likely to be just that it's further away than it looks.
CptReynolds reckons no. 3 is an A320 (like no. 1). If so, they're minimum* 7.5 NM apart and no. 3 is (by similar triangles) 2.5x as far away as no. 1. That makes no. 1 4.33 NM from the observer. We lack metadata and any direction or even time references but this map I found shows plane-spotting locations roughly 300-400 m (or 0.2 NM) E of the visible start of 27L and 27R (I assume the airport is on westerly operations because of the prevailing wind, and I won't consider displaced thresholds). If the observer was at one of those locations, that would mean we have, with rounding, something like:
A/C no. A/C type Min distance from runway (NM)
1 A320 4.5
2 B747 7
3 A320 12
4 ? 14.5
5 ? 17
At this point, I admit to knowing much more about photography, maps etc. than aviation operations, and will let the experts weigh in on reasons (my suspicion is that no. 3 is limiting its speed)
* Of course there will be a margin on top of the minimum, but LHR runs pretty tight so I'll ignore the fact everything is probably a little further away.
The question really seems to be not "why doesn't the 2nd aircraft have its gear down" as "why does the 3rd", given that it's still some way out.