I would cut out those brown branches on your Berberis thunbergii ‘Helmond Pillar’right out. It is not normal for them to turn brown (I presume you are talking about the leaves on the branches). I suspect the leaves of your plant might change to a different shade of red/purple in autumn before they drop off in the winter? This is perfectly normal, in fact deciduous Berberis species are often sought after for their attractive autumn colour. But brown is not desirable, I suspect that wood might be dead, maybe as a result of our summer drought. Cut that wood out, right down to healthy looking wood or right down to soil level if you are unsure. You can do it now, but normally the best time to do it is immediately after flowering, giving the plant a whole year to recover and produce new wood for flowering next year.