What is meant by the term higher education.
it means a "higher" level than you can learn at a school. Schools often teach up to "A" level (which is quite high) or Scottish "highers" though for other reasons many young adults fit in better at a "6th form college" or other institution
"Further" education is when you go on to study after leaving school, but not to Degree level. For example if you left school at 14 and later trained in engineering. One of my neighbours did that, he had formerly been a motor mechanic but is now a project engineer on satellite rocket launches.
It is quite hard work to study when you are used to being a grown-up with a job and a home of your own. I have a nursing sister friend who gained a relevant degree through OU, which was necessary for career progression. She was given study leave and other assistance by the hospital. Something similar often applies to people gaining professional qualifications, for example when I started my career I was part-qualified. You may get your classes and exams paid for by the employer (until you fail one, and have to retake at own expense). A naval officer of my acquantaince taught maths to junior ratings, enabling them to go on to study engineering, navigation and other specialities.
Some people who did not have such opportunity, resent the idea of education and learning for others. Hence slurs like "Micky Mouse." But a poor degree, or one in an irrelevant subject, has been no obstacle to, for example, Prime Minister Johnson (though he is rumoured to resent people who did better).
John Prescott, a former deputy prime minister, left school young with a poor education, but by hard work he bettered himself, and was lucky enough to get Union assistance in gaining more education. He went on to graduate from Ruskin College and the University of Hull. He is in many ways a more admirable man who overcame his disadvantaged origins, than Johnson who has led a priviledged life.
Some politicians know that less-educated people have a greater propensity to vote "Brexit" or "Boris" or "Tory" or "UKIP" and this may influence their support (or otherwise) for good education of common people.