Certainly a lot less than 40 years ago but other than the Wye, Severn and Trent, where else is the opposite true?
I know there are more in the Dorset Stour from the tidal up through Throop, Parley and Longham than many will have you believe. As for the introductions over the last several years, they seem to have done the usual disappearing act although the odd one or two have appeared in the "dipping" aquatic life counts we've carried out. I helped with several work parties during the 2016 closed season and was very pleasantly surprised on Throop to see in excess of a dozen barbel between School Bridge and Barbel Corner. That gave me sufficient incentive to give them a try but only had two (both good doubles) and lost a couple. I had a couple more from the tidal but they were few and far between. Long gone are the days of multiple keepnets full of barbel in the 2lb-5lb bracket but that was 40/50 years ago
mg:
I know less of the Hants Avon but places like Royalty still hold a fair number and regularly produce fine fish. They have had introductions but they were mainly longer ago. Always the odd big fish reported from the Avon between Christchurch and Ringwood but very few appear to fish those areas let alone report captures. The Somerley/Ibsley syndicate above Ringwood includes some very fine anglers and plenty of barbel reported. Similarly above Ibsley produces some fine fish but not necessarily all reported. Likewise above Fordingbridge, some excellent club and syndicate waters all hold a few.
The Test and particularly the Itchen have fair numbers (unfortunately). Especially the lower and progressively higher Itchen has quite a big population including plenty of doubles. Ignorant, misguided (and a few other choice expletives I can't use on here) "anglers" have been responsible for their introduction and those barbel should not be in those rivers!
Inevitable rumours of a barbel or two in the Dorset Frome but, so far, I've not come across one or indeed seen any images of one. I did see a photoshopped image of a barbel purported to be from the Frome above Wareham. But the same angler/fish/pose combination was later seen and that was from Trammels on Royalty!