The toilet tissue is about not having chemicals in it and being highly biodegradable. Coghlans, Kampa, etc. are all known brands. Amazon, EBay, etc., can help you out if your local outlet can't. Its relatively expensive but it's only for occasional use not your day-to-day business.
Note that "biodegradable" is a slightly hit and miss term, biodegradable material typically requires a minimum temperature, and that's why allegedly biodegradable plastics have been found on the seabed after many years as the low temperature inhibited degradation. SO... if you're going at altitude, your best bet is to "doggy bag" it and carry it to lower areas for disposal. Best would be to carry both poop and tissue, but if you can't face that at least bury your poop and doggy-bag the tissue. A well-knotted scented doggy bag is not as bad as it sounds in the outside mesh of a pack. If in doubt don't be scared about double-bagging it. Better to be safe than suffer a split-bag-in-the-rucksack.
Another tip as a dog owner is to NOT bag it up like a balloon, as some people I've seen do, make sure there is very little air in it before tying the top. I know mountaineers put their poop bags into a second ziplock bag, but they're doing multi-day hikes, that might be excessive for a day walker.
What is "at altitude" in the UK? That will vary by geography but a rule of thumb will be the treeline which is claimed to be somewhere between 500-600 m (1700-2000 ft) in the UK.
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EDIT: and I know this not the first time on this forum I have talked a load of s...