I like that arrangement, We still get a Brilliant Stadium for domestic & European cup finals & the odd England game while the England team play around the country for all to watch, whats not to like?
As for the NFL team, hard to draw a comparison as its really only a North American sport (professionally anyway) so its not really the same as say playing a premier league game stateside.
Jacksonville Jaguars would seem a sensible bet to relocate to London, probably called the London Bulldogs of something amusing! I wouldnt be surprised if the NFL team were located in the USA & also had to travel in for home games, Bit like some Russian premier league teams being based in Moscow, Anzi for example!