Golden Fish, здесь лучше сказать "to start speaking IN English with me".
speak English -- это говорить по английски вообще "Do you speak English?"
speak in English -- говорить по-английски в конкретной ситуации. "He doesn't speak Russian, so let's speak in English"
Здесь ситуация тоже конкретная -- говорить/общаться со мной по английски.
http://www.efl.ru/forum/threads/58739/

@Галина, спасибо, это действительно важный нюанс)

my pleasure :)

GoldenFish's translation is the most idiomatic. "start speaking in English with me" is a little clumsy.

То есть, разницы между "speak English" и "speak in English" нет? Я помню, в одной компании, где был англичанин, мы начали обсуждать что-то по-русски, и он попросил нас говорить in English, потому что не понимал. Я с тех пор запомнила, что есть разница.

А-а-а, я поняла, о чем ты говоришь. speak in English -- это правильно, просто моя фраза была построена неуклюже.

First of all, "speak with" isn't the best choice in your sentence because we mostly use this for discussions: "I need to speak with my boss - I want to change departments." However, in GoldenFish's sentence it's different because "SPEAK English with" is used in the sense of "USE English with me" which is more idiomatic, since the speaker isn't looking to discuss anything, but rather to hear another language. Secondly, "in" is only rarely used with languages, unless you're referring to the original language of something: "a movie, article, passage in English" -or- "Shakespeare only wrote in English," but when it comes to speaking, it's more idiomatic and common to not use a preposition.

Uly, you've read my mind. I was just going to ask you about the difference between speak to ant speak with. And thank you for enlightening me as to usage of to speak in.

https://books.google.com/ngrams/graph?content=speak+English%2Cspeak+in+English&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cspeak%20English%3B%2Cc0%3B.t1%3B%2Cspeak%20in%20English%3B%2Cc0

my pleasure. If you ever have a question as to whether something is idiomatic or not, put it in an N-gram. You can add more than one term, separated by a comma.

In this one, "speak with me in English" doesn't even appear on the ngram, so it's safe to say that it's not idiomatic: https://books.google.com/ngrams/graph?content=speak+English+with+me%2C+speak+with+me+in+English&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cspeak%20English%20with%20me%3B%2Cc0

*as to THE usage of "to speak in". -- was in a hurry)
Yeah, I've checked out the Ngram Viewer. A very useful tool indeed, thank you!