I'm sure this subject has come up elsewhere (maybe on World of Spectrum, on StarDot or another retro forum).
Anyway, we need to see inside the case. As there should be the real DC power supply inside. The external power supply is just a mains transformer in a neat plastic case.
The DC PSU can run from either suitable AC inputs, or from suitable DC inputs. The problem is, however, neither type is very common
It is possible to still get custom wound transformers, but I suspect they will be expensive. And you still need a suitable case, plus the need to wire everything up in compliance with electrical and safety regulations.
The easier route is to buy a 12V DC regulated power supply that can supply at least 2A. Then if you can solder, use a "simple" 5V SMPSU chip and four capacitors to generate the +5V supply from the +12V rail. You could even fit the 5V SMPSU chip to the PCB of the existing DC PSU.
Mark

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QL, Falcon, Atari 520STFM, Atari 1040STE, more PC's than I care to count and an assortment of 8 bit micros (Sinclair and Acorn)(nearly forgot the Psion's)