Right, time for an update.....
Rossey very kindly sourced me some new batteries for the APC SURT6000xli 6KVA online UPS which made their way down here courtesy of Hifly and Mark230678
Clearly they were better than the old ones as these had a terminal voltage just over 100V DC each whereas the old ones were less than 12V !!
As soon as I put them into the UPS and connected the power back up, away it went happily.
Here is the waveform on the output with no load, very nice pure sine wave

Here it is in with mains input (not lister power) on the top trace and ups output at the bottom. Notice the UPS output is more pure sine than the mains which has flattened peaks. This is with 1.5KW of load connected as well. The cutoff trace is just down to the timing of the camera shutter, it was a full trace on the scope screen

This is with the Lister powering the UPS and almost no load on (just the scope and UPS battery charging). I dont think I need to mention that the Lister output is the top trace.

And here is the same with a 1.5KW of load connected to the UPS

It bolsters the voltage nicely too.
With the 1.5KW of load connected, UPS input voltage from the Lister was just under 215V as below

but the output was a rock steady 230V

Just to prove it was happy on the messy generator power, here is the front panel. Battery charging and no error lights..

I have tested the Actifry which now runs perfectly on UPS power.
Now to build a cradle for the UPS, test the earthing arrangements and RCD operation now I know it works and connect it up more permanently.