Not STRICTLY true...
A freight terminal was built at Fratton, adjacent to Fratton station (behind the diesel fuelling point), designed for limited container traffic, consisting of a siding & run-round loop/headshunt & substantial roadway access, and a mobile (road) crane; after it had been completed, someone noticed that between Fratton and The Rest Of The World, there were three bridges crossing the track in Portsmouth which weren't able to accomodate container traffic. These were fairly quickly adapted, and the first freight Mon-Fri working (taken off the Wakefield to Southampton Western Docks modal at Eastleigh yard) was on Wednesday 14th January 2009. This was more or less a trial run, with just one empty two-part wagon; the same happened on the Monday; on the Tuesday there were three of these wagons (also empty). The following day, it was one double wagon carrying two Geest Banana containers into Fratton. Most days it was just bananas, but on a number of occasions, rum was in the consist too. It was generally locally known as The Pirate Special. However, this new freight flow, small as it was, began just as the recession started to kick in, and it petered out around the end of February 2009, and hasn't yet restarted. The working from Eastleigh to Fratton was 4T01, and the return (empties) to Eastleigh was 4T02. I made a point of going to Fratton to photograph the first Pompey freight in donkey's years, some pics here & onwards:-
http://daverowland.fotopic.net/p55874575.html
Whole collection:-
http://daverowland.fotopic.net/c1638414.html
Somewhere in the early 2009 collections, there are some pics of the working at Eastleigh.
Let's hope there's an upturn in demand again soon!

PS: There HAVE been two or three HST visitations over the past couple of years in the form of
A) Football specials from the Bristol direction, arriving too late (ie dark) for photos, and
B) The New Measurement Train (Yellow HST), photos in this collection here:-
http://daverowland.fotopic.net/c1669517.html
Hope this clarifies the situation.