You don't have to have the same government to be a spirtual successor, plus the UK is more of a Republic anyway, the King/Queen is a figurehead that doesn't do anything with it's power and if it did they would get thrown out(finally). If the US is Rome, UK is Greece. I feel that fits more but Rome DID decline and eventually fall 1000 years after the loss of "The Empire" so Britain fits well.
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