John brought/has brought some pizza

John comes to Peter's house with a pizza. Peter puts it on the kitchen table, then they have a short conversation, and then John leaves. Then Sarah comes to Peter, they go to the living room, sit down and start talking. After a while, Peter remembers about the pizza and says to Sarah:

1. By the way, Sarah, John brought some pizza, and I put it on the kitchen table, so if you're hungry, I could bring you a couple of pieces.

2. By the way, Sarah, John has brought some pizza, and I've put it on the kitchen table, so if you're hungry, I could bring you a couple of pieces.

I would use version #1 because John has now left and Peter put the pizza on the table when John was in his house. But I wonder if it would be possible to use version #2 in British English in this context (there's a present effect: the pizza is in Peter's house and it's still on the kitchen table at the time of speaking). If both versions are acceptable, I wonder if version #1 would still be preferable in British English for the reasons I've given.

EngLearner said:

I would use version #1 because John has now left and Peter put the pizza on the table when John was in his house.

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That's possible in BrE.

EngLearner said:

But I wonder if it would be possible to use version #2 in British English in this context

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Yes.

EngLearner said:

I wonder if version #1 would still be preferable in British English for the reasons I've given.

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Neither is preferable in itself. The choice depends on whether the speaker is thinking of the past actions or the present states.

We use "slice" when we talk about "pieces" of pizza.

I'm fine with "pieces" as well.

"Slice" is much more common.