because we are not interested in each other's country, the conversation doesn't go anywhere
We don't have a particular interest in each other's country so the conversation doesn't really get started
We are not interested in each other's country so we run out of things to talk about
「お互いの出身国」＝ each other's home country
「興味が無く」＝ not interested in ～ / not have an interest in ～
「話が弾まない」＝ the conversation doesn't go anywhere / the conversation doesn't really get started / have nothing to talk about / run out of things to talk about
「お互いの出身国に、興味が無く話が弾まない」＝ because we are not interested in each other's country, the conversation doesn't go anywhere / We don't have a particular interest in each other's country so the conversation doesn't really get started / We are not interested in each other's country so we run out of things to talk about
イギリス 
