It depends on a few things,
The HTS code for Video Game is 9504 10 00 00 - more info:
http://findhts.com/tariff/search and type video game into he search box.
As the UK is part of countries that are considered OK for import, it is part of Column 1 which states it does not pay any fees at all. However this is subject to a limit, I don't know what this is, only the carrier will be able to tell you this or the custom office in the USA.
Marking the item as a gift and a value of less then $45 guarantees it will have no fees, but by doing this means you will only have insurance of the declared value of $45.
Having just checked it looks like as long as you use the right HTS code then you can import atleast $500 without fees, something I didn't realise before (note to self should check more).
Fees may still be incurred if you put on the box that you have 15 games in there, they will check and open everything and then pass on a bill to you for doing so. Be careful with your wording, be simple and not super detailed.
Write:
Video Game and not
Video game with figurine and steelbook unless of course you are below the $45 limit. Steel book may mean DVD and Blu-ray, which comes under a different classification with fees. That's also a big red sign for custom, who will open it up. As you have a HTS code for a video game and a steelbook maybe a film.
90% of time there are no problems, but should your item be randomly stop and thoroughly inspected, it's best to have all the paper work correct so it leave custom quickly and they are not force to open it up.
I would contact your post office customer service for more info on importing or get the exporter in the UK to contact the carrier for more details.
Also when importing something of this size, Royalmail is not going to be an option, a courier like Parcel force can be used but is expensive, I would use an agent to get DHL to send this out. Much cheaper, quicker and unlike Parcel-force will have full tracking.
Stay Away from TNT who's prices are only small for large companies, Fedex is also only good for internal US shipments. UPS again have some pricing issue but are very close to DHL, UPS will also delay shipment by one day for some reason.
But nothing in my opinion is better than DHL, only talking from my own experience with all of them.
hope this helps.