Most UK spec cars will have had the battery backed sounder.
I recommend getting rid of them at this point - as by now the batteries will either have failed entirely, or be failing. And in the worst case, as you've found out - overheat and cause a fire.
I replaced mine with a standard 12v siren, and set the BECM alarm sounder settings to 'klaxon' so it will drive it properly. If you're not fussed about having a sounder, you can just disconnect it and be done with it - though may need the procedure as Gilbert has stated above if its still working.
Southampton with a Nanocom for Thor/GEMS P38s
1996 4.6 HSE, then became a 4.0, now cubed.
1997-8 4.6 HSE Motronic/Wabco prototype vehicle. Now M57 powered. Still auto.