87018 was used when HM Queen Elizabeth II officially opened the Preston-Glasgow electrification in 1974.
For the Silver Jubilee 87003 was used for the Scottish tour in May 1977 and 87004 was used for the North-West tour in June 1977.
These were all before the locos were named.
87002 did work the Royal Train at least once while named "Royal Sovereign". There's a picture here at Crewe in May 1983, which I suspect is an ecs move after taking the then Prince of Wales to the Kyle line for launch of an oil platform.
Crewe: passing through with the Royal Train 14/05/1983. Rescanned.
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In steam days 61671 was named "Royal Sovereign" and was Cambridge's Royal loco. 61671 hauled HM Queen Elizabeth II on journeys to and from Sandringham many times in the first few years of her reign.