That's the point in London directly opposite where you are.
Imagine walking in a straight line to the centre of London, and then carrying on for exactly the same distance in exactly the same direction. That's your London antipodes.
n.b. I've taken the centre of London to be the King Charles I statue at Charing Cross.
n.b. I'm aware that the word 'antipodes'technically only refers to opposite points on a sphere, but it'll have to do.
It's exactly as far away from Charing Cross as my house in Bow, and extraordinarily different. To get your bearings, Castelnau lies on the Barnes peninsula, inside a great meander on the Thames, and grew up after the opening of Hammersmith Bridge in the mid 19th century. The flamboyant villas of Lonsdale Road are a delight, owned by fortunate upper middle class families who've never needed to transform their homes into flats. My precise antipodes is opposite the entrance to St Paul's School, outside a villa now used by the Czech/Slovak community which has two entirely unofficial blue plaques stuck on the front. The locale is quiet, leafy and comfortably white, very much not like Bow E3 at all.
The Olympic Stadium lies 1km north of my house, so its antipodes are 1km south of Lonsdale Road. It turns out the precise opposite of the Olympic Stadium is the Red Lion pub in Barnes, by the 5-way junction at the turn-off for the London Wetland Centre. As for the antipodes of Stratford station, that's at the other end of the High Street, on the waterfront immediately alongside Barnes Bridge. Gustav Holst lived here, in an elegant cottage on The Terrace, but moved out just before he wrote The Planets. Again this well-to-do Thameside backwater is a huge contrast to Stratford's bustling cosmopolitan hub, but that's geographical opposites for you.
So how do you find your London antipodes?
The simplest 'old school' method is to get a map of London and a long-enough ruler. Line up your house with Trafalgar Square, and then measure exactly the same distance in the opposite direction. One catch is that you may not have a map large enough, and another is that you may no longer own a paper map, because this is the 21st century grandad.
Measuring lines on digital maps is harder, because that's progress, unless you happen to have tools for drawing lines on your screen. I opened up a Google map and plonked a marker at Trafalgar Square, then tried to draw a single straight line from my house so its midpoint landed on the marker.
Or if you like maths and geography you could play around with latitude and longitude in a spreadsheet using a clever formula. To help you get started, the centre of London is at 51°30′26.41″N, 0°7′39.56 W (or 51.507335, -0.127655 in decimal), according to the Wikipedia page for Charles I's statue.
Some more examples.
» The antipodes of Buckingham Palace is the Royal Courts of Justice. It's exactly as far east from Charing Cross as Buckingham Palace is west.
» The antipodes of the Houses of Parliament is Tottenham Court Road station. It's exactly as far north from Charing Cross as the Palace of Westminster is south.
» The antipodes of St Paul's Cathedral is Knightsbridge.
» The antipodes of the Tower of London is Kensington Palace.
» The antipodes of Kings Cross station is Nine Elms.
» The antipodes of London Zoo is Camberwell.
And that last one is why I find this concept fascinating. I always picture London Zoo as being within central London and Camberwell outside, but it turns out they're both the same distance out. Admittedly the West End runs more to one side of Trafalgar Square than the other, but the overall concept still holds.
Let's head out a bit further out.
» The antipodes of Stratford is Barnes.
» The antipodes of Brixton is Gospel Oak.
» The antipodes of Wimbledon is Walthamstow.
» The antipodes of Greenwich Observatory is Harlesden.
» The antipodes of Wembley Stadium is Lewisham.
» The antipodes of Penge is Finchley.
And a bit further into the suburbs.
» The antipodes of Chingford is Motspur Park.
» The antipodes of Hampton Court is Hainault.
» The antipodes of Croydon is Cockfosters.
» The antipodes of Heathrow Airport is a large area south of Hornchurch.
» The antipodes of Romford town centre is Feltham Young Offenders prison.
» The antipodes of Orpington is Bushey, Herts.
Again what's interesting is the number of times you think "Oh, I never realised it was that far out" (or "not that far out", depending).
And we can go further.
» The antipodes of Harlow is Dorking.
» The antipodes of Gatwick Airport is near Stevenage.
» The antipodes of Southend is Reading.
» The antipodes of Cambridge is Worthing.
» The antipodes of Oxford is Canterbury.
» The antipodes of Ipswich is Southampton.
And further still.
» The antipodes of Birmingham is on the French coast at Le Touquet.
» The antipodes of Paris is in North Lancashire near Carnforth.
» The antipodes of Swansea is on the island of Zeeland in the Netherlands.
» The antipodes of Londonderry is near Strasbourg.
» The antipodes of Edinburgh is in the Loire Valley.
» The antipodes of Stornoway is in the Alps near Grenoble.
London is very much in the corner of Great Britain, and a lot of the continent is much nearer to us than a lot of our own country.