Never saw that. Sounds a lot like the Nicholas Cage movie "Knowing" People knew the world was ending and they all started hugging and junk. I'd probably be in the process of something a bit more intimate with the first cute woman i came across.
Not at all.
The world has long been abandoned and the human race spread throughout the galaxy. The only way the earth has been still around was the field holding the sun form expansion. Sense the earth was unpopulated, the feild was being shut down. An old space station that orbited earth was outfit for people to go to the main deck and watch as the earth slowly gets eaten up. Rose, the current companion and The Doctor, a man Rose has just meet that evening had just traveled from 2005 to the last day of the earth to see it go up in fire. Unfortunately, the last pure human ( the rest had been breading with other people such as cats and trees [ tree hugger lul] ) had decided to kill everyone on the station because she is just that much of an evil, self loving bitch. The Doctor and company decide to stop her by doing stuff.
TL;DR Earth gets incinerated, people forget trees, and the last "pure" human, who happens to resemble a trampoline via plastic surgery, tries to kill people.
Also, the tardis is bigger on the inside then on the outside.