Broken English refers to using the language incorrectly.  It is not applicable to common small grammatical errors,  but rather major grammatical problems of incorrect use of words, incorrect verb tenses, improper use of articles, etc., usually with a very limited vocabulary.  

In my opinion, Pidgin is different and includes mixing words of more than one language and very simplifies grammar and vocabulary.

Broken English is an informal term and may not be specific enough for linguists. This may be why you have not found a formal definition.

An Interesting question. I hope to find the answer too

Yes. I sometimes ask myself if my own performance in English could illustrate it in a native speaker's eyes!

The answer to this question is another question:

What is the difference between broken English and Pidgin English?

I remember that as a child while learning English in Nigeria, "incorrect" English was considered "pidgin" or "broken" English.

However, Pidgin English has found a place in linguistics for historical reasons.

The term "World Englishes" which particularizes the varieties of English spoken by peoples in different parts of the world seem to take care of the concept of broken English. Especially since broken English was (?) often used in the sense of "corrupted English". An interpretation which does not conform with modern thoughts on language use and development.

I think we can speak of Pidgin in the countries where English was imposed on the local people, usually in former colonies, whereas broken English seems to me to apply to anybody who is able to use just very limited vocabulary and grammar, and this only with errors.

But well, does it include struggling beginners? I don't know. 

Broken English refers to using the language incorrectly.  It is not applicable to common small grammatical errors,  but rather major grammatical problems of incorrect use of words, incorrect verb tenses, improper use of articles, etc., usually with a very limited vocabulary.  

In my opinion, Pidgin is different and includes mixing words of more than one language and very simplifies grammar and vocabulary.

Broken English is an informal term and may not be specific enough for linguists. This may be why you have not found a formal definition.

I agree with Michael Marek's comments above.  'Broken English', in today's terms, is an old-fashioned and informal term, which takes us back to Colonial arrogance!  

Pidgin as used in the Pacific Islands (eg. Tok Pisin - PNG, SIPijin - Solomons, Bislama - Vanuatu) are all formal languages with grammar and rules and which draw from language roots including Portuguese, local languages, English, French etc.  

I could say that as a Native English speaker, my Pijin is a 'broken' form of Pijin because I am still learning to communicate effectively - which to me is the basis of learning a language.  I am now using 'Broken Lao' - luckily I have enough to get by, but couldn't possibly study or read in that language!  (I empathise with all students learning in their 2nd, 3rd or subsequent languages). Fluency takes a lifetime!

 Hi, I  think it is when the speaker trying to dilever meaning without paying attention to the correct forms.  It sometimes comes as a result of educational system that promote communicative competence without making balance with linguistic competence. 

After-thoughts, further to my previous comment, - I think it is other second language speakers who probably are more likely to use 'broken English' as a derogatory label.  Not all language learners are doing so for academic purposes and therefore communicative competence has a place.  Particularly as it is most often used in terms of speaking, anybody with the confidence to try to speak in a new language to communicate is on their way towards linguistic competence if that is where they want to go.  Too much attention on 'correct forms' can prevent a person from daring to open their mouths!

I asked about broken ENGLISH because this is what I was actually looking for but certainly, it could be any other language.

I am not sure if the phrase sounds (or is meant as) derogatory, I rather notice the element of effort in it.

I completely agree that one can only learn a foreign language through mistakes in performance that's why I have doubts if the label can apply to the learners' communication, but then who knows if the speaker is a learner or has reached the final stage of his or her competence?

For me, broken English is English which lacks accuracy and fluency, and is characterized by interference of native language grammatical rules as well as rules of use.; however , it reaches a level of understanding by others though with some effort.

I think this term could be explained differently among its users. Sometimes, we use this term in Iraq even when we speak perfect English but with some Arabic words, phrases or sentences which is mostly used in informal meetings. We also use this term to describe someone's poor English.

Yes, exactly, it can mean some very different aspects and levels of command of English. I sometimes wonder how efficient communication is possible since we use words and labels with no clear meaning.

Dear Lucyna Wille,

The term Broken English is frequently used in India as Most of the cases many of the Indians the regional speakers use few words in English and majority of the words in regional language so as to communicate with others where only English need to be spoken like offices etc.,. They use this sort of communication  by using the content words(In English) to reach the main content to the listeners, and they don't follow the grammar rules too due too lack of grip in English grammar.. Generally this sort of communication is called broken English.

The grade-4 employees who are uneducated use such type of broken English to communicate with the officials who know only English. This sort of broken english is observed When the Western country people visit India, the vendors use broken English so as to sell their goods.

Hope My answer is apt to the question. Please feel free to give any further feedback.

With regards,

Pavani Sasidhar.

Thanks Pavani. Do you think it is justified to attribute "broken English" to people with little education who have grasped just as much of it as absolutely necessary to be understood?

Dear Lucyna, Absolutely I don't agree. But it happens when Situation demands in some circumstances in countries like India as there are many people who work for  their livelihood without having proper education. So, In such cases I do agree with the scenario.

Pavani Sasidar