Down packs a bit smaller, but in these thin garments, it doesn’t really save much weight. Add to that the fact that you are likely to be sweaty when you pull it on, and it might be wet out too, and synthetic is far and away the better choice (yes, I have both).
I assume you are in the UK?
Here in the US Enlightened Equipment is both less expensive, lighter and warmer than Patagonia et al. And you choose custom colors, fabric weight and sizes.
Unfortunately I assume shipping and tax/duties will make it very expensive to the UK.
For warmer weather a vest/gilet is a great option, it offers the best in warmth : weight/packed size ratio. Of course I assume you will have long sleeved, wind/rain shell all ready.
The big thing is to save weight and packed size by minimizing features like pockets. The next thing to look at is fabric weight. Ideally, for something like this you’d go ultralight: a 7 dernier fabric. That will be (very) hard to find in big commercial brands. 10d would be ok too, but 20d or thicker is really a waste of space and weight for something like this.
Are there cottage brands in the UK that make stuff like this?
If not, check the usual brands:
decatlon for cheap.
Montane, RAB, Montbell, Karpos, Haglofs etc. Often these can be found on sale too.
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