Yes, that's correct - it was Woolworths quite a number of years ago but Debenhams took all the old Woolworths stores about 3 or 4 years back.
We pop through Ledra Street now more often than we take our own vehicle through, especially since they put the insurance cost up. We have a Mazda double cab/pickup truck and last time we took it through by the racecourse at Ayios Dometios it was around 50 EUR.
If you're going through Ledra Street don't forget to pop in and have a mooch around Buyuk Han (previously an Ottoman travellers inn) or you may find a series of posts I put on my personal blog of photos taken during the Kataklysmos public holiday in June this year of interest. This link will take you to them and some short video footage of Buyuk Han:
http://cypruslifeinpictures.wordpress.com/tag/nicosia/