Could Thatcher still rise in an altered Commonwealth?

In a continuing British Commonwealth, how likely is Margaret Thatcher still to come to power?

Margaret Thatcher might still rise because she was influential, though the altered political system creates too many changed compromises and contingencies for a confident prediction.

The scenario does not automatically remove Margaret Thatcher, since an influential politician could still find a path to power. Her real career cannot be assumed to continue unchanged after the Commonwealth's political structure and earlier events have diverged. The compromises required to win office might differ, as might her conduct after taking power. Once enough causes have branched, a counterfactual has to admit uncertainty about familiar later outcomes.