The respected Institute of Fiscal Studies has raised the spectre of a two-nation Britain, after finding that some of the poorest households are facing much higher inflation rates than average. You may catch a preview of the publication in http://www.ifs.org.uk:80/publications/4455. Otherwise you need to subscribe (which I do not).
The main reasons are that households have different spending patterns. The items of consumption of poorer households (such as rents, domestic energy costs, public transport, food and leisure services) have experienced substantially higher inflation than richer ones. The big drops in average inflation are due to mortgage interest payments and the decline in private transport (falling petrol bills). These have proportionally affected the rich much more than the poor.
The Institute finds that in January this year, the richest fifth of households had an average inflation rate of negative 1%, while the poor fifth had a positive rate of 5.3%.
This evidence appears to confirm that a recession can impact badly on the level of income equality in places like the UK and USA a situation likely to worsen with growing unemployment. As the OECD pointed out (Income inequality and poverty in most OECD countries), inequality also tends to suffer over the upswing of the cycle (more particularly in the USA).
The Institute warns that the economy may recover in a year or two, so the inflation experiences may conceivably be reversed.
That said, if we had a proper wealth distribution measure, which allows for the recent erosion of capital appreciation, we might get a different story.