I would say that the reason most Brits order one or two drinks at a time is
for politeness. In the UK drinks in bars or pubs aren't usually more
complicated than beer, wine, simple two-item cocktails like gin and tonic,
vodka and coke, etc. When asking for more complex drinks in Britain it's
reasonable to expect that the server will have to think about or ask what's in
them, and I guess the habit carries on abroad. Also, what Americans might call
a Screwdriver would just over here be called a vodka and orange, so you might
end up with an order like 'a vodka and orange, a gin and tonic, an Archer's
and lemonade, a vodka and coke and a whisky and water', which is more
confusing than 'a Screwdriver, etc.'. However, for an order like 'two glasses
of white wine, a pint of beer and a vodka and coke' most people I know would
say it all in one go.
We're not being offensive if we ask for one thing at a time, we're just trying
to make it easier for the bartender. If I were working in a bar over here, I'd
feel most comfortable making one or two drinks at a time. Most Brits don't
expect their bar staff to be well trained as many are students or part-time
workers just making some cash in their spare time, and as I said most people
would order fairly simple things like two pints of beer - cocktails aren't too
common over here. I do agree that asking for, say, a margarita and then when
it's made, another one, is dumb. But I don't know anybody who would knowingly
do that....