According to a recent study, London is the fourth most expensive city in the world behind New York, Hong Kong and Geneva. The trip itself is expensive but becomes more affordable in January (and its sales!), and by avoiding Christmas and summer.
The plane and the bus are often cheaper than the Eurostar but, in all cases, book six months in advance – no more for low-cost flights which will not yet be on sale. Want breathtaking panoramic views without paying €35 for the Shard? Come for free to the Sky Garden, or the Duck Waffle restaurant.