Here is the short version. Most standard comprehensive car insurance treats putting the wrong fuel in as driver error, not an accident, so plenty of policies simply do not cover it. Some do, either as accidental damage or a specific misfuelling benefit. The only way to know for sure is to read your policy's product disclosure statement, or ring your insurer and ask.
Even when it is covered, there is usually an excess to pay, and on most policies that excess is around the same as a straightforward drain, sometimes more. A claim can also affect your no claim rating next year. So for a simple wrong fuel drain, a lot of people are better off just paying for the job and skipping the claim altogether.
Some roadside providers do not cover a misfuel drain. Your membership may include towing home or to a workshop, but check before relying on it. We can attend the car after a tow. If it is a hire car, notify the rental company and get approval before arranging work.
The one thing worth knowing: the big bills come from driving on the wrong fuel, not from it sitting in the tank, and that damage is the hardest of all to get an insurer to pay for. Draining it early, before you drive, is the cheap and certain path. Keep the engine off while you decide. If it is a hire car, notify the rental company and get approval first, then call us. See our petrol in a diesel and diesel in a petrol pages for the mechanical detail.