I happened to be working in the City of London this morning and I noticed that aircraft going into Heathrow were approaching the airport from the east, yet aircraft going into London City were approaching the airport from the west.
This is not that uncommon.
Heathrow operates what's known as a "westerly preference". That means that even in a light easterly wind (or any wind with a light easterly component), 27s are still the preferred runway. In those conditions LCY will probably be operating on easterlies as you don't really want to land there with a tailwind.
Heathrow Noise: Westerly preference