You can definitely bring both coffee and trail mix in. I like to have either nuts or trail mix with me to start with. I used to wake up hungry during my first night and the trail mix was good to have until I could get to a store.
Most of the hotels I've stayed in in Britain only have 2 packets of regular coffee. I bring my own because I often want 3 cups, lol. Plus depending on the brand offered, mine tastes better to me. IF you like sugar in your coffee bring individual packs of those too because sometimes there are only 2 or 4. I have gone to drinking my coffee black unless the coffee is awful, lol but I still carry sugar packets.
With a cursory look I could not find where the UK rules address dried fruit except for this link which says dates are fine.
https://www.gov.uk/bringing-food-into-great-britain/fruit-vegetables-nuts-seeds