We sold ours on ebay recently. Have been using ebay for many years.
We listed the car as a classified ad, which is a better idea than going to auction. You will get cheeky offers from dealers from all parts of the UK trying their luck, most of which won't even bother to come and view it. A genuine buyer will live close by, and is more than willing to come look at it before putting an offer in. List it for as long as possible and don't sell until you are somewhere near your asking price, assuming you have researched beforehand what similar cars are going for, and have gone for in the past. If it's a good car, with a reasonable asking price with not too high a mileage it will have a lot of interest, so don't sell to the first person who puts in a low offer - you will likely get more.
Put as much information as possible to avoid stupid people asking stupid questions, and try not to oversell the quality, especially if its got a few scuffs and things. Try and be honest. All used cars have an issue or two, but stating these up front means the buyer has little comeback if they find a fault.
Always consent to letting them have a mechanic give it the once over. If they want to take it on a test drive, go with them and take someone with you ALWAYS. Make sure they pay cash and give them a receipt. Dont take an uncleared cheque.
Good luck. Let us know how you get on.