This is a charade - multiple wordplay elements are joined together in sequence to build the answer.
You need to reverse a Soviet/Russian limousine (3 letters), then add an anagram of 'rusts' (indicated by 'badly'). The result should give you someone who aspired to be like Margaret Thatcher.
Answer: LIZ TRUSS | Reverse ZIL (Russian limousine) to get LIZ, then add TRUSS (anagram of 'rusts' indicated by 'badly'). This gives the former PM who modelled herself on Margaret Thatcher, the original Iron Lady.