yes, but if you go throught you own insurer, even a no fault claim, it can affect your premium.
Going directl;y through the other insurer all youll need to do is notify your insurers for their records. They then do nothing further and you get all sorted in one go by other insurers. It will also help in the fact that Direct line will pay for everything and you wont then need to claim things like car hire from them.
If you were near renewal date it would also be good as you wont have a claim outstanding. For instance, if your insurance was up for renewal this week you would have claim outstanding and your premium would increase until it was settled, regardless of whos fault it was.