Am I breaking the law by home schooling?

Yesterday, at the UK border agency, the agent asked my kids where they went to school.  When I told him I was homeschooling my kids, he said "It's the law that they must attend school in the UK".  I mumbled something about my husband's job only being one year, so we opted out of UK school, and he let us go, but it got me wondering - am I breaking the law?

Home Schooling is perfectly legal: http://www.direct.gov.uk/en/parents/schoolslearninganddevelopment/choosingaschool/dg_4016124

Thank you, WebyJ.  That is very reassuring.

The right to educate your child otherwise than at school was enshrined in the 1944 Education Act ... I believe that, at that time, school attendance was compulsory in many parts of the United States. 

"The parent of every child of compulsory school age shall cause him to receive efficient full-time education suitable ;
a) to his age, ability, and aptitude, and
b) to any special educational needs he may have,
either by regular attendance at school or otherwise."
(Education Act 1996, incorporating the 1944 Education Act and later legislation).

That last phrase in the legislation, quoted above, gives rise to the name of the organisation in the UK that supports home education; Education Otherwise. 
http://www.education-otherwise.org.uk/