Deer should be treated respectfully in the UK if you happen to see any of the species (Personally saw a young Roe deer buck holding some rutting ground in my local forest.) We have Red, Roe, Fallow, Sika, Water deer as well as Reeve's muntjac. Some of the larger deer obviously have antlers over the autumnal months and can be agressiveaggressive during the rutting season but the likelihood is when out walking they will run from you - the issue here is being careful at night when driving they can come running out across the road (happens to me at least once a month) and they can go through a windscreen if hit. Also for dogs not used to deer, chasing them (also known as worrying) can lead to conviction and fines.
Badgers should be avoided whilst out night walking, again more commonly when out with dogs, due to their ability to destroy footpaths / walking routes with their dens, creating risk of a twisted ankle or worse. Near where I live badgers have almost completely collapsed a footpath by digging dens underneath it, which is something to watch out for. The likelihood of seeing one would be slim however, but dogs who like running down holes should have an eye kept on them. As a note they also are likely to be a bTB carrier (bovine tuberculosis).
Some people can worry about their dogs as Myxomatosis is a threat in the UK to British rabbits, but it. It is not a threat to dogs or humans, but is toit can infect pet rabbits - so try not to handle wild injured rabbits if you see them unless aiming to take them to a vet or the RSPCA/SSPCA for treatment - and. And if you do thisneed to handle them, anti-bacterial hand sanitizers will help prevent spread of infection.