Hello Ian,
It depends on the age of the car. Older diesels don't mind a drop of petrol mixed in of you can drain out the majority and then fill it up so that it is as dilute as possible.
Newer diesel engines (in the last 4 years or so) are not so forgiving. The best thing to do is have it done by a garage as the fuel filters and possibly the fuel pump will need to be changed so that no long term damage occurs.
It sounds like you have started up the car and run it so the garage option is probably the best. Some newer cars even have a sensor before the fuel hits the engine and will cut out if the wrong type is detected.
Petrol is more refined than diesel and will cause damage to a diesel engine. It can strip the engine of lubricant and cause it to seize.
Whoever told you of the potential large bill was right unfortunately. However getting the petrol drained out before you put too much fuel through will be less expensive. It is a time consuming job as fuel lines, filters etc have to be cleaned or replaced. Petrol tanks are usually accessible from bolts under the flooring of the car which takes time to get at.
One tip I would give you is that if the car is still under warranty, don't get the work done at any branch of the dealership. Putting the wrong fuel in will void the warranty on certain things and give the dealer enough cause to point the finger if anything else goes wrong with the car!
The £6000 bill is probably a dealership price and you should be able to get it done cheaper.
It is an expensive mistake to make, but one you won't do again!

I'm completely understanding how you feel

Let me know how you do with it, I speak from experience (and yes, I was daft enough to get towed back to the dealer!).

My experience caused me to investigate this type of accident and I was staggered to find out the in Watford (where it happened), more than 50 people a week do exactly the same thing.
If the nozzels on different fuels were different shapes, eg petrol=triangle, diesel=square etc and an adaptor was available on each pump to fit into the car, the thought process about shape would stop this mistake.It is however impossible to put diesel in a petrol tank because the nozzle is too big to fit in the car (apparently). I suppose the fuel companies are unwilling because for one reason, this mistaake means that they can sell twice as much fuel. Not only do you have the repair bill and the cost of throwing away the offending fuel, but then having to buy a new tankful.
Regards
BF Nicky