On exterior brick the finish question is really a breathability question. Brick and the mortar around it are porous by design — they soak up moisture and release it again. Whatever you put on top has to allow that to happen, otherwise you trap water behind the film and end up with blown render, spalling brick and peeling paint within a couple of winters. So the finish you want is a matt, breathable masonry paint. Avoid gloss, satin or anything that boasts about being "sealed" or "waterproof" in a film-forming way — those are the dodgy ones for brick.
From the supported range, Little Greene Intelligent Masonry Paint is the one I'd reach for first. It's properly breathable, dead matt, and the colour depth is a cut above the trade options. Dulux Heritage also does a masonry finish in their exterior range, and Sandtex (a tool brand, fine here) is the reliable workhorse if you're covering a big elevation on a budget and want something that's proven to last 15 years.
For colour, keep it grounded and don't fight the brick. A soft off-white like Farrow & Ball Pointing or Slipper Satin reads beautifully on a painted brick cottage. If you want something with more body that won't show every streak of weathering, Mizzle or a stony Ammonite sit handsomely against red or buff brick.
The "but what about" here is prep. Masonry paint lives or dies on it. The brick must be clean, dry and free of any old unstable coating or efflorescence — brush off, treat any fungus, and let it dry properly. If the surface is chalky or powdery, a stabilising primer first is non-negotiable. Don't paint in the cold or with rain due within 24 hours.
And a word of caution, mate: painting bare brick is a one-way trip. Once it's coated it'll need repainting every decade or so, and stripping it back later is a nightmare. If the brick's sound and handsome, leave it be.