"A lot of customers who would previously have turned their noses up at 99p and think, 'We don't need to go there,' are now a bit more open to paying a visit," says Hussein Lalani, commercial director of 99p Stores.
A widening customer base is not the only benefit from the downturn.
"A company selling homewares went into administration earlier this year and within three or four weeks, all these guys started turning up who had bought all the stock from the administrators and were clearing it to us," says Mr Lalani.
Poundland's founder took the idea from dollar retailers in the US and opened his first store in Burton-upon-Trent in 1990.
Running a store in which prices cannot change at all presents interesting challenges, because even with inflation at 5%, it is difficult to change all the signs to read "everything is £1.05".
'Everything is a pound' has become a popular concept
There is no shortage of pound stores in parts of the country, and on one small stretch of a shopping street in London's West Ealing can be found Poundland, 99p Store, £1 Superstore and Mr Pound.
Some shops have abandoned the pound idea altogether, with certain retailers embracing a new "everything is at least £1" concept, which does not feel like discounting at all.
But the chains such as Poundland and 99p Store are sticking with their pricing policy and finding other ways to cope.
"We sell 48 pencils for £1 with a rubber tip on but it wouldn't be difficult for a company like ourselves to take that down to 45 or 42 if the price of pencil lead or rubber rose," Mr McCarthy says.
The advantage that the chains have is that manufacturers of brands such as Wrigleys chewing gum or Colgate toothpaste are prepared to make specially-sized packets or tubes for them that they can then sell for £1.
Inflation has also meant that there are products that they could not previously sell that are suddenly on their radar.
Sometimes I wish we could charge £1.05 or £1.10
Hussein Lalani, 99p Stores
Things that cost 90p in supermarkets a few years ago would not be a bargain in a pound store, but now they have gone up to above £1, they become a possibility, so Poundland is currently considering selling eggs, bread and milk.
"Hopefully next year, you will see even more products available that are particularly relevant to the value-conscious consumer at a time when their disposable income is most under pressure," says Mr McCarthy.
"We are perfectly positioned for the flight to value."
Another way that pound stores try to battle inflation is by buying their products from all over the world.
I would lose the magic if I changed the pricing policy
Jim McCarthy, Poundland
Poundland was criticised earlier in the year because its store in York was selling Polo mints bought from a unit of Nestle in Indonesia when the factory that made them in the UK was less than a mile away from the shop.
"If we could get them from York at the price that we could get them from Indonesia, then we would," says Mr McCarthy.
It later emerged that the mints were transported by ship, not by air, so the environmental objections were less valid.
But buying stock from overseas opens the stores up to currency risks, which is a problem, because prices cannot rise to make up for currency fluctuations.
At the moment, the pound is at a five-year low against the US dollar, which makes imported products more expensive.
There is some currency hedging and when the shops make big advance orders for Christmas products, for example, they will buy the currency to pay for them straight away, even if they do not need to make the payment for several months.
But this problem is nothing new, according to Mr McCarthy.
"We have operated when the dollar has fluctuated between $1.30 and $2.08 to the pound and have always managed to deliver amazing value," he says.
If single-pricing is a problem for currency fluctuations, it is a help when negotiating with suppliers.
"Often a supplier will say he can't do anything on the price and I'll say, 'I can't buy it - it's quite simple,'" says Mr Lalani.
"He'll go away and think about it and come back and do a deal."
As inflation remains a problem, there are signs that stores in the US are abandoning the pure dollar store idea.
Some items in 99p Stores are below 99p, which upsets pound shop purists
Some of them have started selling items for higher prices as well and some have transformed themselves into regular discount retailers.
Mr McCarthy at Poundland admits that when he first started, he considered whether to start selling merchandise for different prices, but soon decided against it.
"I would lose the magic if I changed the pricing policy," he says.
Meanwhile, 99 Cent Store caused ructions in the US last month when it raised all its prices to 99.99 cents.
Its counterpart in the UK is not changing for now, but is not ruling it out either.
"Sometimes I wish we could charge £1.05 or £1.10, because then it would open up a whole new range of products that we could do," says Mr Lalani.
"We're sticking to our guns for now - let's see what happens in the future."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.