two please

Hi,
During spring sort out I decided it would be esier to care for things if I knew what they were.

The first I would like to identify is one I have not planted, it grows in a shaded area between a conifer and ivy. It gets no winter sun as it is against an Easterly fence. It has whitish hairs on the leaves so it looks almost frosted.
It has been a pest in the front garden where it pops up in the grass. I'd like to know what it is and if I should keep it or not.

Plant B is one I unearthed in my old garden, transplanted into a pot then moved it to its new location last year where it seems much happier (next door but one to mystery plant a). It has lovely glossy green (evergreen) leaves and purplish blue flowers in the summer. I have been treating it to ericaceous compost mulch which it seems to like (when the leaves went yellow).

Thanks
David

 

Think that the first one might be more likely to be Centauria, (cornflower) maybe?

 

I think the first one is Cornflower and the second one is some kind of a hebe.

 

Thanks guys.
The potential hebe has Buddlea type blooms.

D

 

second pic is definately a hebe