Deadheading the flowers would help. There is some green in the same places.

At first sight I would have said that lack of water might be a problem but perhaps your shrub (hebe?) is just coming to the end of its life.

Does look like a Hebe seriously affected by drought earlier on... not much you can do at this time of year - you can try cutting it back hard in mid spring, if its still alive next year.

A wise bloke asked by Monty Don about why he didn't grow buddleias said that they grow beautifully but die really badly. I've got 5 buddleias & he's right. They look crap late in the year.
Your choice to accept a plant that dies off in an ugly way is your choice. Though it may not always be that bad if you can get something else to sprout & cover it up?

Darren8 - Hebes don't die badly, as you put it (though I think you mean die back rather than actually die) - this one is evergreen and usually makes a neat, mounded shrub. The browning is possibly due to drought... and its the leaves that have gone brown, not the spent flowers, by the looks of it. Either that or its got some problem at the root, or its just very old.

That is what I meant Bamboo. You're correct. But if a plant isn't doing well considering a replacement is an option?

Absolutely! But if Lornachan is very attached this plant, waiting till spring to see what happens is probably worth it...

And stuff goes on...

Thanks everyone for your advices, I would leave it till Spring and see how far it would recover, I am now sure how old the plant is, it was there when we moved in 10 years now. Much appreciated.