There is a very well established auction house in Nottingham (about 75 miles from you) called John Pye.
They are into the type of items that you have mentioned, but you would have to make some kind of inventory, as you would not get anywhere near a fair price if you merely listed it as games "stuff".
I'm being a bit flippant, but the more detail you gave as to the contents of the containers, the better the price you should get.
Breaking it down into much smaller lots would also open up a larger potential audience.
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