The reason for the distortion was obvious when I removed the speaker driver unit. The surround that supports the driver cone had crumbled away in quite a few places on the right speaker and almost completely gone on the left speaker. The surrounds were in several pieces resting on the speaker grills.
The rear of the speaker drivers are labelled Technics EAS-15PL403A 8 ohm. Lots of searching the web produced a few results that told me people had contacted Technics and were told it was no longer in production.
I figured any speaker driver with the right impedance and power rating would do. I did not know the power rating so I guessed about 40W. There are many speaker drivers that satisfy this requirement so I decided to look for one that had the same (or as near as possible) fixing holes. The nearest I found was the Visaton BG17. I purchased mine from RS Components for about £15 each.
You can see how the Technics units compare to the Visaton units from the top (previous section) and from the bottom (this image). The fixing holes differ by only a couple of millimeters so with a bit of screw manipulation, the existing holes could be used.
The only snag in the whole of this was the Visaton units have different sized crimp tags to connect the cables. The negative lead for both units is the same size on both drivers so there is no problem there. Luckily, I had a bag of crimp connectors that fit the Visaton so I used those. If I had not had any, I would probably soldered the connection.