It is way more historically significant than my last London flat which, before me, was occupied by Mrs Madge Pules, a Tottenham charlady.
The successful applicants may even get a glimpse of Princes William and Henry who have offices in the palace. They may also be lucky enough to score a royal ballpoint pen.
Please don't fret too much if you are not accepted. I have some other accommodation options for you. The only negative: there might be a lengthy commute if you were hoping to catch any of the events at the Games.
Do a quick currency conversion and you can compare the value of staying in the Royal Penthouse Suite in the President Wilson Hotel, Geneva. Nightly rate is only $53,000 (I'm sure that will be US$.)
What do you get for that? Well, for one thing, you get stunning views over the city, Lake Geneva and Mont Blanc - all through bulletproof windows! I wonder whether Her Majesty thought of that little detail!
If you wanted to have a few friends around for dinner, that's no problem: the suite's dining room seats 26 people around an oval mahogany table.
If you don't want to spend that much but still want to be a mere Lear jet flight away from the Games, you could check in to the Penthouse Suite at The Martinez Hotel in Cannes. This will only set you back $18,000 per night.
Features there include an open bar, private butler and limousine on call 24 hours a day. You also get silk curtains which you can draw to block out the view across the entire Bay of Cannes.
But, if you'd rather stay in New Zealand, you could, for a fraction of the prices above, book a room at Huka Lodge. A single room during the high season will only set you back $1930 but for that you will get pre-dinner drinks and a five-course dinner. Please note GST is not included but I think it may be available on request.
Still too pricey? I could get you down to around $100 in one of Palmerston North's fabulous themed motels: choose from mock crenellated castle, mock Tudor or just plain mock. You will, however, have to endure generic instant coffee in little sachets and tiny tubs of long-life milk.
Failing that, we're down to rock bottom and I don't think my last option would be suitable for a queen. Unless perhaps she chose to dress down a little.
I'm talking about a backpackers' dormitory in Wellington. It's cheap and you'll need your own bedding but there are showers available. There is a communal TV lounge but the TV is currently only working on channel two unless you jiggle the remote a bit which brings in little bursts of Prime.
And please be aware that, at such a bargain price, the windows are only made of standard safety glass. They are not bulletproof. As they say, beggars can't be choosers.
Wyn Drabble is a teacher of English, a writer, public speaker and musician.
