The company, although well versed in selling children's literature, only entered the market for general books 18 months ago but already claims to have eclipsed chains such as Books Etc, Ottakar's and Hammicks.
Only the big high-street names - WH Smith, its sister company Waterstone's and Dillons - and academic specialist Blackwell's are ahead of it, according to Leslie Henry, research director at Book Marketing, a market research company. While Smith is well out in front with estimated annual sales of pounds 250m, Woolworth's total of nearly pounds 50m make it a contender to take over fourth spot from Blackwell's.
The company claims to have sold 11 million books last year, giving it 5 per cent of the market, and hopes to double that figure this year.
For some authors - including bestseller Catherine Cookson, whose latest book, Tinker's Girl, sold 80,000 copies at Woolworth's stores - the company claims it has accounted for up to 20 per cent of the book's sales. It has also sold 250,000 copies of the AA Road Atlas.
The abolition of the price fixing cartel last September has a been a disappointment for both doomsayers and optimists. Predictions that it would destroy British literature have proved false, while promises that it would dramatically increase readership have fallen equally short of the mark.
"It does not appear to be having a huge effect on the total number of books sold," Mr Henry said.
Most up-market retailers ignored the end of the Net Book Agreement and continued to sell books at the publishers' recommended prices on the theory that any increase in market share would be more than offset by falling margins.
Discount booksellers have tried to profit from the end of the cartel, but none have done as spectacularly well as Woolworth.
The company immediately launched six 1,000sq ft specialist book departments and now plans to open another 22. Another 740 of its 780 shops are equipped with smaller book racks.