Do American PS Vita games play on UK PS Vita console?

Sony gaming systems (PS3, PS Vita) are all region free so you can buy games from any country and play them on any machine.

Yes, they do. All Sony PS3 , PSP and PS Vita are region free for running games. Region there only means which of your PSN account's country selected, which is a software issue. Everyone is able to register multiple regions PSN accounts but only have ONE ACCOUNT ONLY enabled to the PSV console, or re-set to manufacturer default is needed. Note: PS3 console does not require any re-set and can have multiple PSN accounts on file on one system. No matter which countries release you bought for the console, it runs any countries release of games. Therefore gamers benefit the choice for getting cheaper imports or games not sold/released in their area. Simply remember this: 1. Any countries released PSV, PS3, PSP consoles run any countries released games. They all play exactly the same way. 2. Region is the choice of PSN account & games disc selected ONLY, and not related to a console at all.

Yes you can buy and play US games, the major thing everyone fails to mention is that in linking a US game to the UK account you will NOT be able to get DLC for that game because it is from the US, so if you ever want online play or DLC for the games you might want to buy them in the UK.