アメリカやイギリスの発音に近づけたいって英語でなんて言うの？

If you "lose your accent", it means you now speak with a different accent. When you first started speaking English, you may have had a heavy Japanese accent. With time, your Japanese accent may become faint.

Formally, losing your accent is called "accent reduction"

In order to inform one's teacher that you would like to sound more American or British you may ask in the following way;
DearTeacher My Goal Is To Have A British Or American Accent, Please Advise Me On How I Can Achieve That.
Dear Teacher, Please Give Me Advice On How To Make My Pronunciation Sound Like The US Or UK.

Make Your Goals Clear And Ask For Advice on how you can achieve it.

Well, it is a gallant ambition, although most teachers would probably stress to you that clarity should be the main goal rather than simply trying to emulate an accent.

When you want to explain to your teacher that you want to work on your pronunciation to a point where it's as closest as possible to native English speakers in the UK or the USA; you may says this in the following ways:
-I want to make my pronunciation sound more like English speakers, as people from the USA or the UK
-I want to improve my pronunciation to a point where it sounds more like native English speakers in the UK or the USA

Pronunciation is the way we say words or the sound words make when spoken so as well as saying 'pronunciation we can also say we want to 'sound' like
A native English speaker is a person who speaks the language of the country they were born from birth

"I'd like to speak with an American or English accent" tells your teacher what your request and required result is.

"I'd like my pronunciation to be similar to that of an American or British native speaker" gives your teacher a clear goal to work on.

"I'd like to work on my pronunciation. I'd prefer to speak like a native English speaker" is another way to tell the teacher what you'd like to work on during the lesson and again gives them a clear idea of what your desired result is.

If you wanted to explain that you want to get rid of your Japanese accent and speak like a native English speaker, you can say any of the following: "I want to make my pronunciation closer to that of a native English speaker, for example from the USA or UK", "I would like to speak English in a native way, rather than a Japanese way" or "I would like to sound like a UK or US speaker rather than Japanese".