My current car came with an unwanted private plate of the previous owner.

If you contact the registration buying companies they'll give you two prices - one (the higher) as them acting as a broker to find you a buyer, and a second lower price to buy the plate off you.

The bit about 'charges if the plate is sold elsewhere' are there so that if you market the plate with a second company then the first company still get some fees paid if you sell it through the second company (if that makes sense)

I'm always dubious about these valuations though. For example, let's say you've got a plate that's REALLY worth £1k. I run a plate selling company. I tell you it's worth £1.5k, just to get you to sign that contract. A year later, someone offers £1k. You are now sick of the thing, so accept. I get my fee, my competitors don't.

You could just put it up for auction through ebay with a reasonable reserve (think how big the selling companies fees are, and what you'd end up with, then knock 10-20% off that for 'offers'), and see what happens.