Ratings agency Moody's warned late on Monday that the reform would be "credit negative" for the sovereign because it would compromise the bank's autonomy.
The pound gained after the UK and European Union agreed on Sunday to continue Brexit talks and the EU's chief negotiator said a deal was still possible.
The dollar was down around 0.2pc against a basket of currencies at 90.621 at 0804 GMT, staying within December's ranges but not far from its lowest since 2018.