Hi, BA
the Montane Pac Plus Gore-Tex Jacket might fit the bill, it seems to get a good write up at a price near your budget. I see they are selling at about £150-£180 so shop around. £158.99 at Ultralight gear which gives free postage and are very reliable to deal with, I have used them to buy quite a few things.
I haven't got one of these jackets but the spec's look good at the price.
I use a Rab Latok Alpine jacket for through hikes, it is dearer but reviews suggest it is particulary good for ventilation and high activity, I do like it, and have used it on two long hikes.
For day hikes with possible showers I use a RAB super Kinetic, which is incredible light and stretchy, but gets damp in heavy prolonged rain, especially at Ruck Sack contact areas. I have used this on one 200 mile hike but although I love the jacket found it wanting in a heavy torrential shower between Fort Augustus and Newtonmore.