In this schematic of a Soyuz rocket, the payload fairing is depicted with the flag of the USSR on one side, and what appears to be the flag of the United Kingdom on the other.
Did the Soyuz ever fly with the UK flag on it?
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Here's a photo of TM-12 on the launch pad with the UK flag visible.
Several nations partnered with the USSR and sent astronauts to Mir during this time period, and in each case the appropriate national flags were painted or decaled on the launcher.