Over 100,000 Turks were smuggled into the UK by just one gang:

Eight suspected leaders of a people-trafficking gang thought to have smuggled up to 100,000 Turkish people into Britain were arrested by police yesterday in a series of early morning raids. Detectives described the gang as the most prolific people smuggling network they had encountered.

Other large smuggling operations that have been shutdown include:

• The Snakeheads, a group of Chinese criminals, is one of the most notorious people-smuggling gangs in the world. Jing Ping Chen, better known as Little Sister Ping, was jailed in 2003, and is thought to have been responsible for smuggling between 150,000 and 175,000 people earning about £12m.
• In May, a man and woman involved in smuggling people out of India to work at fish-and-chip shops in Shropshire were jailed. Charan Singh, 48, above, was sentenced to 15 months after he was found driving an immigrant. Bakshinder Chatha, 35, helped an illegal immigrant get a national insurance number and was sentenced to nine months.
• In May 2004, a gang which made thousands of pounds by offering a "club class" service to hundreds of illegal immigrants they brought into the Midlands was jailed. The ringleaders were sentenced to five years. Immigrants from India sold land and belongings to raise fees up to £11,000 to be smuggled through ferry ports before being dropped at their chosen destination as part of a "door-to-door" service. They were "fed and watered" and transported in people carriers by the West Midlands-based gang who were caught in a joint British and French operation codenamed Gular. Most of the gang were arrested in June 2003 after police swooped on vehicles carrying 14 illegal immigrants in a lay-by near Canterbury in Kent.

Yeah, 100K is small compared to what we have but the population of England is only about 50 million and that is from just one source.  The population of the United States is estimated to be nearly 300 million now.

This brings up an interesting thought.  If a single gang can smuggle in over 100K people (who require air, water, food, and waste removal during their transit) just think how easy it would be to smuggle in 10 to 20 times that many firearms (roughly the same mass) into the country. The only limiting factor on the number of firearms in the UK is the number of willing buyers with the money.  Once again restrictions on firearm access only disarms the victims.