If you want something that will be properly water proof, it will need to have taped seams, and
for it to be properly breathable it will need to be a rmembrane fabric like Gore-Tex or Event, rather than the coated fabrics which advertise 'breathable' but in reality will be a sweaty plastic bag. You can't get anything like this for £40 or less.
I would look at the outdoor mountain/hill-walking ranges from companies like Berghaus (they always fit UK users well) or some of the membrane hunting jackets from the likes of Harkila, though these will be expensive.
I've been wearing GoreTex jackets for decades for outdoor hillwalking and general wear, but the most breathable jacket I have is an eVent (the breathable fabric) jacket from Montane. I've shot with this wearing a heavy fleece underneath and still been comfortable.
One disadvantage with jackets like this is you don't really blend in with the cammo hordes
Another thing to be aware of is many 'outdoor activity' waterproof shell jackets are shorter in length these days as they are designed to be worn with waterproof trousers, so you may want to look for a more 'high-street' user type of jacket with a bit more length, again Berghaus cater well for this sort of market.