Some salmon will have started their run by now, fish caught early in the year are called "springers" and are more likely to be found in the lower reaches of a river. As the year moves on more fish enter the river, and more fish move up towards the head of the river. They enter the river between February and November, but it is very much dependant on local geographical and seasonal differences. On the upper Wear I think the fish get here by winter, and I saw a dead, spent fish of about 5lbs in the shallows in March I think, though to be honest I couldn't say if it was a salmon or sea trout. My kids saw and photographed one in a tiny burn at spring half term.
I'm guessing that it could take them up to a year to travel the length of the river but spawning in the shallow streams seems to take place in March on this river.