I am desperately trying to find the title and author of a sci-fi book I read in the 1970s. The story goes something like this...

Scientists on a planet discover, via the spectrum of their local star, that it is going to go supernova (or possibly red giant). A fleet of giant spacecraft is constructed and these escape to orbit, carrying some of the population with them. One ship is damaged in rioting which breaks out on the planet but still makes it to orbit.

The spacecraft leave the planet's orbit and escape the system. The damaged craft explodes. The people on the other ships then watch the end of their star. As time goes by the ships get further from each other as their wave front expands. Contact begins to be lost with craft one by one. On one ship the deduction is made that the ships are being picked off by encounters with predator civilisations as all the ships are heading towards the galactic centre where it is presumed the density of other civilizations will increase. The ship is turned round and heads towards the outer rim of the galaxy. Finally the ship lands on the planet Earth before the rise of industrial civilisation on Earth.