With regard to the UK, this quote is from the Royal Horticultural Society:
Known as the butterfly bush, the fragrant flowers of buddleja are a
favourite nectar source for butterflies. These undemanding, mainly
deciduous shrubs, deserve a place in every garden with their
spectacular displays of blooms and honey scent.
No mention of the plant being invasive.
Here is the RHS list of invasive non-native plants covered by the EU Regulation on Invasive Alien Species (which still applies to the UK). Again, no mention of buddleja. There's a lot of scaremongering associated with so-called "invasive" plants. Not surprising really, as frightening house owners provides a living for businesses who eradicate those plants (the second link provided by @Jurp being an example).
I had a Buddleja davidii in my garden (20 miles north of London) for several years. I got rid of it not because it was invasive, but because it was too big for the available space (even after cutting it hard back each spring). Walking the local streets I can see no evidence that my ex-buddleja has self-seeded and taken over the neighbourhood.
My advice is not to believe everything you read in The Sun and enjoy your buddlejas.