I suppose any plant that does well and spreads can be called invasive. We could just as easily call them 'successful' plants. However, if we want to maintain a varied collection of plant species and a lot of different habitats for invertebrates and other creatures, we have to 'control' the dominant plants to give the others a chance.
So the hogweed with its statuesque seedheads is one.
And creeping thistle with its creeping roots and it seeds carried by fairies - or thistledown more prosaically.
The Friends of Filnore Woods expend a lot of energy trying to prevent brambles taking over the grassland. At the end of the summer they send out these long looping stems to root in the grass and form new plants. (The brambles, I mean, not the FFW.)
Even oak and ash, the main trees at Filnore, keep trying to turn grassland into wodland.
Acorns planted by jays produce tiny oaks that if left become mighty trees.
And ash trees produce so many ash keys that they can turn up anywhere.