Because London isn't a sovereign nation.
Obviously this isn't going to happen, there's no reasonable mechanism by which London could gain independence. But if there was, I'm pretty sure London would go for it
Scotland has been its own traditional country for a very long time, and the union with England was formed when the King of Scotland became also King of England and not the other way around.
Northern Ireland is the vestige of a brutal occupation of Ireland by England. The Catholic population traditionally loyal to Ireland now outnumbers the UK-supporting Protestants.
London has never been a country. This is obviously a protest demonstration and not a serious proposition.
Whilst the argument is for all of London to be independent. It would surely be possible for the 'City of London' to remain in the EU.
What is or is not a sovereign nation is not an immutable fact of nature, and the Brexit vote may change that.
Though Scotland is more likely than London to get away.