Very common occurrence!
The tip is NOT to use a main dealer or any of the breakdowns specialist "fuel drain" guys, they are extortionate & there is no need. I know of a BMW owner who ended up with a £5k bill including a new fuel tank as he was told the tank was "polluted indefinitely".
If you have a good quality local garage they will simply use an electric pump to drain the fuel straight through the system bypassing the filter, flush the system with an additive, fit new filters, refill & drive away, average of appx £200 + the replacement fuel (dependant on the the disposal fee which depends on the local council). I used to do them at the roadside but this is no longer allowed due to the spillage & disposal rules, takes a bout an hour or 2 at most.
As for damage limitation, if you realise what you've done before you start the engine then even easier as there's only the tank to drain. If the vehicle has been run petrol in diesel won't hurt too badly (will clear out the channels nicely!) but diesel in petrol tends to sludge things up as it's an oil based fuel so you may need new plugs etc. Only real complication is the modern day electronic systems may need resetting as they will show a "fault" even after the drain out.