This adapter in reality is just a step down transformer from 240V mains input to a 24 volt output capable of supplying current of 1 amp. In theory any transformer supplying that power output would do but you should look for one that is sealed and will fit inside the space you have. If you have the skill with a soldering iron you can cut off the special jack plug and solder it on to the leads from the transformer. No polarity is involved as everything is ac. Not a difficult job for a reasonably skilled electrician.
Do you know what the correct name is for a sealed wired unit.
Tried using the words, power, line, sealed, stair lift, mains, battery charging, with the word Adapter, and Adapter on its own. Also it’s size all though I can get round this as there is plenty of room.
It’s the three pin plug I would cut off and connect to the fused wall outlet the jack plug goes to the stair lift.
The stair lift has four strips top and bottom so when the chair reaches its two stopping points it charges up the batteries.
If you can point me to a suitable adapter that would do the job as my knowledge is limited.
Lorraine's link is a good one. As an alternative here is a used one for a Stannah stairlift click here but I am sure that there may be newer ones available, just make sure that the output is 24V and capable of supplying 1 amp.