By David Milliken LONDON (Reuters) -The Bank of England’s independence will be put to the ultimate test as it seeks to bring inflation back down to its 2% target from more than 9%, Governor Andrew Bailey said on Tuesday. The cost-of-living squeeze is a big political issue in the contest to replace Boris Johnson as prime minister, and some Conservative lawmakers believe the BoE was too slow to raise rates and wrong to continue asset purchases until last December. “I’ll be quite simple about this: I think overwhelmingly the most important demonstration of Bank of England independence is that we …