The claim by UKIP's leader is not true with respect to education.
In the following I will follow the US State Department's wording for "immigrant"/"nonimmigrant": immigrant visas are visas for the purpose of "[living] permanently in the United States" as "a lawful permanent resident" (source), so all other visas are considered "nonimmigrant". That means "immigrant" will refer to persons who are residing, or intend to reside, on a permanent or indefinite basis in the United States. This is different from the usage in that article, which seems to call workers on temporary work permits "immigrants". The State Department would call them non-immigrants, because their stay is temporary.
(Neither usage is "more correct"; it's just a question of semantics, and this answer covers both immigrants and non-immigrants.)
Public school access to non-citizens
Dependents of immigrants and temporary workers in the United States are allowed to attend public elementary and secondary schools ("K-12"). Tuition is free, not paid directly by immigrants, according to USCIS's "Welcome to the United States: A Guide for New Immigrants", page 50:
Public schools are free ... Your federal and state income taxes and your local property taxes pay for these schools.
According to the Department of Education's guidance, this even extends to illegal immigrants.
In fact, dependents of persons present in the United States on most visa categories are allowed to study at public K-12 schools. According to the Immigration and Customs Enforcement's document "Nonimmigrants: Who Can Study?", the only exceptions to this (who are not allowed to study in public K-12 schools) are dependents of those in the US on the following non-immigrant visa categories:
- Visitors (B) (though in some cases they can still study)
- Aliens in Transit (C)
- Crewmen (D)
- Foreign Media Representatives (I)
Minor children of those on all other visa categories can study at public K-12 schools. This includes temporary workers (class H nonimmigrant visas).
Possible source of confusion
Perhaps UKIP was confused by the following. According to the Department of Homeland Security,
An F-1 student may attend an Student and Exchange Visitor Program (SEVP)-certified public high school (grades nine through 12), with certain restrictions:
- For a maximum period of 12 months – This time limit includes all public schools the student attends. You cannot spend a year at one public high school and then transfer to another.
- Must pay the full, unsubsidized per capita cost of attending the school district. Payment of this fee must occur before the child applies for an F-1 visa. You must be able to present proof of this payment is at the visa interview and at the port of entry when you apply for admission into the United States.
However, this applies to only those on F-1 visas, which is a non-immigrant visa to attend school in the US. (Translated into common terms, this means "exchange students can only study as part of their exchange program", not a general policy for all non-citizens.) Their dependents are not subject to these restrictions, as they have F-2 visas, not F-1 visas:
A minor F-2 or M-2 dependent of an F-1 or M-1 student may attend public school at the appropriate grade level without any additional permission or documentation from SEVP.