An example of the perfect infinitive

When one British native told me that this sort of infinitive doesnt exist I tried to defend myself. I tried to give example sentences, f.e. ''To have written this article was a big mistake''. It didnt work! The person went on assuring me this thing doesn`t work in English.
One more possibility to prove they exist was another native who used this grammar. Simon Reeve in his ”Pilgrimage with Simon Reeve (2013)”, Episode 3 said it!
Here it is, that evidence!
Когда один британец сказал мне, что такого инфинитива нет, я попытался защищаться. Попробовал дать примеры в предложениях вроде ” Написать (to have written) эту статью было большой ошибкой”. Не достучался! Этот человек продолжил убеждать меня в том, что такая штука в английском не работает.

Additionally, there are many other signs, like the Cambridge Dictionaries site article
or this famous Russian site.
Вдобавок, есть много других знаков, вроде этой статьи на Кембриджском сайте или на этом известном русском.

To make the meaning of this construction clear here is an extract from the BBC site:
” Remember, we use the present perfect to describe something which has been (recently) completed and still has a bearing on present and/or future circumstances:

I have recently returned from India. To have seen the Taj Mahal in the early morning sunlight will always be something I shall never forget.”

P.S. Using the perfect infinitive is not considered correct grammar by some natives. When they see the perfect infinitive they say something like this: “the sentence you quote does sound believable. My gut instinct is that the gerund is standard but the infinitive a regional variant somewhere. I wouldn’t recommend it since it does sound a bit strange to me – but perhaps it’s acceptable somewhere else.

In other words, choose the -ing form better, i.e. do this: GOING to the Taj Mahal in the early morning sunlight will always be something I shall never forget.

26 Oct 2014, Voronezh, Russia.