Is English actually a pidgin or creole?

In a way, one could argue that Middle English was indeed a form of pidgin, it, of course, stems from a time where contact with French was self-evident.
Couple that with the reasons why we have pidgins: basic, commercial communication requirements and it is very likely that at some point there was a business oriented subset of some language (either English or French) that was the pidgin of the day. However, it's fair to say that nobody was born into that language, and thus it never further developed into a creole.

Of course, there being an actual pidgin is just speculation. What I dare say is that, IMO, Middle English still was a Germanic language, that just got over-seasoned with Romanic vocab.

The adoption of foreign vocab is, though now receding rapidly, has long been a trait of English. As I seem to recall, English is one of, if not the, richest language(s) in terms of vocab.
Owing to its speakers having had encounters with people across the globe, they have adopted thousands of words, from many, many other languages, including Dutch (nautical terms, for example), German (ie aspirin), India (Cumin, mango), African languages doubtlessly had their input, too.

Wherever these encounters occurred, it's very likely a form of a pidgin-like language cropped up (in some cases there are creole languages that prove this). These pidgin-y thingies resulted in new vocab that got added to the English dictionaries, but then you could say that the fact that sailing had a far more profound effect on English as an actual language (need for short, and clear orders -> short sentences).

Ah well, if English were a creole, then surely American or South-African English are far more likely candidates to be branded as such, because in both cases the influence of Dutch has left a clear mark.

This is not really a full answer, since I don't think I'm qualified to describe the historical development.

However, I think it's interesting and possibly illuminating to compare English to a language that is uncontroversially classified as a French-based creole: Haitian Creole.

According to Wikipedia, Haitian creole exhibits the following characteristics:

• 90% of the vocabulary is of French origin

• verbs are not inflected for tense or person

• 3 types of copula, but none inflect

• no grammatical gender or any kind of adjective agreement

• plurals all marked by the same postposed plural word/suffix

English exhibits the following characteristics:

• apparently around 29% vocabulary of French origin, 29% Latin, 26% Germanic (Wikipedia)

• verbs are inflected for tense and number; each verb has at least 4 forms (plain, -(e)s, -ed and -ing) and a sizable number have 5; there are various classes of irregular verbs, including strong verbs that have inherited Germanic ablaut vowel alternations

• copula "be" has 7 distinct inflected forms

• no grammatical gender or any kind of adjective agreement

• a number of adjectives can be inflected for comparative and superlative, a handful irregularly

• plurals mostly marked by a regular suffix; some irregular plurals that are clearly inherited from Germanic for common words such as men, women, children, feet, teeth, geese

My opinion has probably biased what I put on this list, but to me, it doesn't seem useful to classify these as having developed in the same way. Obviously there are different creoles and Haitian Creole might not be the most representative.

A creole does not necessarily, or even typically have a very mixed vocabulary, as you can see from that 90% number given for Haitian Creole. Pidgins (and the creoles that develop from them) are supposed to emerge from language contact where a large number of second-language learners incompletely acquire the grammar of the learned language, resulting in a large amount of simplification and later restructuring when the language is acquired as a first language (the creole).

English is not a Pidgin language like Unserdeutsch, but it is a Creole or Koine Language. I don't know of too many languages that aren't a creation of Koineization or Creolization. Hence Danske, Greek, Latin and Germanics are Creole languages in whole than obviously there is no debating whether English is Koine as well. If all religious symbols are signs of Creolization and the loose circular coins in your pockets stands for Creolization then obviously the language you speak is also per Creolization. Just about every nation speaks some form of Indo Koine or Africaan Kreol unless you live in the Amazon or place like that. Matter of fact I don't even think a person can truly learn and full grasp American history without knowing some form of Creole because the Settlers all spoke some form of Kreol regardless of where they came from.

If so, when did it Middle English stop being such>

I am tempted to say "Three twelve pm on Tuesday 23rd April 1578"... The transitional evolution of a language is a continuum. The continuum continues today.