My experience has been this:
I took up a permanent position with a company in Jan this year. In July this year I began PPL training. I informed the company of this and they conferred with the Death in Service provider, who said no problem (risk seems to be spread across the wide range of people who work for the organisation).
Then I informed the Life Company who hold my personal life insurance that I had begun training. They replied to say that there was no increase in the premium, however, if I renewed or took out a new policy with them, they might consider rating it as I would have to disclose it as part of underwriting.
Basically, my advice is advise your life company. For most existing policies it shouldn't be a problem and will save your loved ones a truckload of trouble if they have to make a claim as a result of a crash.