Sterling was last down 0.27% at $1.3202, showing little change on levels traded earlier, while holding steady against the euro, which traded at 0.867 pounds.
Benchmark 10-year UK gilt prices were also relatively steady, leaving yields up 1 basis point on the day at 4.85%, unchanged from where they were prior to the announcement.
British share indexes held steady after the announcement with the blue chip FTSE 100 index a whisker lower on the day, and mid caps down 0.5%.
Pressure had been building on Starmer, whose popularity among voters has tumbled over his handling of the economy, for months.
Focus is expected to turn to who Burnham picks as finance minister to take over from Rachel Reeves, who has fought hard to retain the trust of bondholders in her ability to keep UK finances on track.
