Dialogue in King's Speech

[Sambodia]

Hello!
When Anthony replied to his Father I'm fine, did it mean that he was ok, he could help; or did it mean that his brothers were ok, he didn't need to help them.
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LIONEL
Can't you help your brother with the washing up...

VALENTINE (Lionel's middle son)
I’m fine.
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Thanks in advance
Sambodia

[Bennevis]

I'm fine - the more polite way to say "No, get lost."

- Hey Jim, want to buy my scooter?
- I'm fine. (Get lost)

Urban Dictionary: I'm fine

But if you say "I'm fine with it", it may mean "OK, I'll do it".

[Sambodia]

Many thanks to both of you, great answers!
Sambodia

[Barb_D]

I'm sorry, I just don't agree with this.

There is no implication of "get lost." It simply means "I'm fine without any additional help."

In modern lingo, we'd more more likely to say "I"m good."

Do you need help with the dishes?
No, I'm fine. // No, I'm good.

Remember that this movie is set at the dawn of WWII, so modern usage reported in the Urban Dictionary is not going to be applicable.

[Bennevis]

I'm sorry, I just don't agree with this.

There is no implication of "get lost." It simply means "I'm fine without any additional help."

In modern lingo, we'd more more likely to say "I"m good."

Do you need help with the dishes?
No, I'm fine. // No, I'm good.

Remember that this movie is set at the dawn of WWII, so modern usage reported in the Urban Dictionary is not going to be applicable.

I didn't get who is who in that context.
Is the guy saying "I'm fine" the one asked for help or the one who needs it?