Is it true that M.Eng. is considered an undergraduate degree in the UK? If so, why?
It is considered an undergraduate degree because no degree is required in order to start the degree. Undergraduate masters degrees are increasingly common in the UK, due to the funding system. Postgraduate taught degrees are not currently eligible for government funding, so an integrated masters degree is often the cheapest route to a masters degree.

The integrated MEng degree developed early, since an accredited masters is a requirement to become a chartered engineer in the UK. Such courses, at least in theory, include the content of a bachelors degree, plus the content of a standalone postgraduate masters degree, often with an option to abandon early and receive a bachelor's degree. PhDs, MScs and MPhils almost invariably require a degree as an entry requirement, hence they are postgraduate degrees.