I've done this flight, as I suspect many have. No FPL, booked out from EGMC, PPR (joke!) from the other end, and off we go. IMC found part of the way, so I told whoever I was talking to that I was now IFR, and carried on. Maintained 2400 feet till clear of London, then 3400.
"Radar Control Service" here and there.
A total non-issue.
A similar flight in the USA, IFR FPL filed, flew it, also a total non-issue.