Trade In

I asked in a previous thread about 1.6 engines and buried this in it as well, I can't see anything else on trade ins on the search of the threads so:

This is my first time with a car to trade in, how does a garage value the car for these purposes and would they give a different allowance depending on whether I was buying a new or used car? I checked on CBG and Autotrader and I realise that the prices given there are 'retail', do they bear any relation to what you could be offered and can you argue over a value offered for trade in?

It's an 03 Leon Signo (front fog lamps, electirc stuff front and back, full service history, timing belt recently changed etc.) 51K miles.

I brought a car for trade in that would sell privately for 13-15 or with dealer 14-16k based on many months tracking prices.

I eventually got 10k on a trade in from a main dealer.
Main dealer then sells on to a smaller dealer so Id imagine you would get better trade in value from a smaller dealer who may resell the car himself.
Obviously a private sale will give you best value.