One UN seat would be the logical extension.
But I would think that would require Britain to adopt the euro.
I'm not sure what one currency or another would have to do with it- if they're one 'diplomatically', one diplomat represents the interests of the one EU.
I imagine a unified Euro block with more than one UN seat would leave open the possibility for those seats to express different opinions and thus become a source of divisiveness within the EU. But I don't know, maybe the currency thing is really that important to them.