"27th October, 1982" is definitely a correct way of reading it.
Take what I say next with a grain of salt, because I come from a place that uses the month/day/year format.
I think that, at least colloquially, it is acceptable to just say the numbers. For example, when the pharmacist asks my mother her birthday, she'll just say "four twenty-one sixty-four." This is also how some well-known dates are commonly referred to, such as "nine eleven." I wouldn't use it in formal writing, but I think that simply saying the numbers is acceptable when the context indicates it's a date.