It's generally assumed that increased trade with countries which have lowly paid workforces must necessarily increase income inequality here: for the low skilled workers in our own economy will be competing with those lowly paid and lowly skilled workers elsewhere, while more highly paid workers in the domestic economy face no such pressures.
And this is true of course, to some extent. The question is, to what extent, and further, are there any mechanisms which offset this increase in inequality?
Using household data on non-durable consumption between 1994 and 2005 we document that much of the rise of income inequality has been offset by a relative decline in the price index of the poor. By relaxing the standard assumptions underlying the representative agent framework we find that inflation for households in the lowest tenth percentile of income has been 6 percentage points smaller than inflation for the upper tenth percentile over this period.
They actually find that some two thirds of the rise in income inequality in market incomes is offset when you look at consumption inequality instead.The reason for this is that goods preferentially consumed by the higher income groups (mainly services) have had a higher inflation rate than those preferentially consumed by lower income groups (largely physical products). We can see this anecdotally in the UK as the varous papers try to calculate "middle class inflation rates" and the like, they all being much higher than the headline rate. It's also closely tied in with Baumol's Cost Disease, in that we always expect productivity in manufacturing to rise faster than that in services and thus the latter to become more expensive in relation to the former. Globalisation just exaggerates, rather than causes, this.
These figures are for the USA but there's one thing that makes me think that the rise in consumption inequality would be even lower in the UK. That is that, to a much greater extent than the US, health care and education in the UK are free at the point of use: it's roughly the top 10% of the income distribution which pay for these things privately, everyone else using the NHS or the State school system. That 10% will have seen the higher services inflation rate while the 90% will not have (except of course for the taxation to pay for it, but that is skewed towards the higher earners as well).
There may well have been a rise in income inequality as a result of increased international trade, but when we measure it by what actually matters, consumption inequality, there doesn't seem to actually be very much of it.