Malaysia is a former British colony so it is natural that British English is spoken here. English is not spoken by all people, however, and certainly not with the same expertise. As an American I don't have much of a problem understanding British or Australian English and, with the exception of a few die hard colonialists who are irritated by American English, they don't have much trouble understanding me. There are actually only a few differences such as lifts instead of elevators, lorries instead of trucks, queue instead of a line and differences is spelling, such as colour, programme, defence, honour etc with the extra letters we don't have in American English. So basically there isn't a problem.
There are a number of International Schools in Malaysia, with most adhering to the British system, while The Dalat School, here in Penang, being one of the few American style schools teaching American English. The locals are amazed at how I can tell which school a child goes to just by listening to them speaking English.
Other than British English, American English and Australian English there is one other form of English that is widely spoken and a little more difficult to understand at first. This is Manglish, a combination of Malaysian and English. Manglish has a different intonation where simple declarative statements sound more like questions and often incomplete sentences are used. For example, "on the light" or "open the light" and "off the light or close the light". Instead of you can't do that they simply say "cannot" or "can can" for you can do that. People ask you to "borrow me a book" or "fetch me from the airport". Instead of going out of town people here go "outstation". When you need a piece of paperwork stamped, you get it "chopped" here. One of the most common terms you here in Malaysia is"lah" at the end of sentence, such as "what do you think, lah". This reminds me of my French-Canadian relatives who say "eh" at the end of many sentences. It doesn't take long at all to understand Manglish. I compare it to talking with someone from Mississippi.
Until recently English was the mode of instruction in Malaysian schools in the subject areas of math and science. English was replaced by Bahasa Malayu, the mother tongue of the Malay population. English is still taught in the international schools and the Chinese schools, but not in the public school. You can notice that most all Chinese and Indians speak English, while the Malays don't speak it that much. I can notice too, that when I speak with older Chinese people their English grammar and conversation is excellent, whereas the younger children and teenagers speak terrible English, because it is no longer taught.
Because English is no longer used in public schools, many parents turn to private English teachers. In Malaysia we have "tuition teachers" who teach a variety of subjects. In the US tuition is the name given to the payment for your education. We use tutors to help those who are not doing so well in certain subjects, but here they are necessary for the children to receive a better quality of education. (This is not my opinion but what has been told to me by the locals). Since there are many students who want to take English, there are a number of people who are willing to teach it. Unfortunately many of these people are unqualified to teach the language. I have seen numerous fliers advertising English classes, where the spelling and grammar are that of a 9 year old. Many of these teachers have learned English from people who themselves do not speak proper English. With so many British, American, Canadian and Australian expats living here it is a shame they can't be used to help teach English to students or anyone else who wants to learn.
All in all living in Malaysia for an expat from and English speaking country is easy, communication wise. I have never been in a situation where I could not understand or be understood. Of course the simple thing to do would be for the expats to learn the local language. You have a choice of Bahasa Malayu, Tamil, Hokkein Cantonese or Mandarin! For me, I am brushing up on my Mandarin.