It's unlikely. The wires of your telephone line are very thin and are close to ground at enough points to first vaporize before they can hit your washing mashine.
Let's assume that the ADSL modem is WiFi only and that there are no cables connected to it except for the phone line and mains.
If there is any vector for damage to your washing machine it's through mains, anyway.
Generally, lightning strikes into cables close to you are far rarer than people think they are (no, anecdotes don't change that). The likelihood of telephone lines being hit is smaller than that of power lines, because these typically hang higher for isolation purposes.
Multiply that with the small probability that damage to the phone system will propagate any further than the point at which the telephone line enters your house, and you'll find that you're worrying about something that is far less likely than your building collapsing onto your washing machine, computer and TV.