Putting the 'ass' in assault
"I don't think a semi-automatic actually counts as an assault riffle, I thought to be an assault riffle it had to be fully automatic, and those are banned even in the USA."
In WWII, assault rifles were either bolt action or semi-auto (M1 Garand). There's even a government program set up to sell Garands, Springfields, and sometimes even Enfields (M1917 rifle) to folk here. So, yeah, in a way, I have a government issued assault rifle, with a certificate with President Clinton's sig on it it. Cool!
As for owning full auto weapons, sure. One has to get a Class III license. This is signed off by both the FBI/BATF and your local/county law enforcement. Now, some counties' Sheriff will not sign off on Class III licenses at all. Is county policy set by county commissioners. One way around this is to form a corporation (LLC) and then have the corporation get a Class III license. I believe that corporations don't depend on local LE sign off. I know of a collector who's done this. Is not the cheapest thing to do. He's on the board of a bank and owns a construction company. Not the type to just go nuts. He's also had a bank safe built in his house (which is also alarmed like a bank) as his gun room. Says his collection is worth almost $1M, if he was to sell off.
Also, Class III weapons are very expensive. Usually run $2000-$3000 on up. Most regular folks, who want to own such things, tend to get the semi-auto versions. You can find just about any type of military arms sold as a semi-auto version. For myself, I'd like to pick up a semi-auto M2 .50 cal.