The official Government advice for people with pets is available here The advice for those walking dogs on behalf of someone not able to is:
“You may also leave your house to provide care or help a vulnerable person. This includes walking a dog for someone who is unable to leave their house because they are self isolating or being shielded. You should remember to wash your hands before and after handling the dog and keep 2 metres away from other people and animals, including when handing over the dog to the owner.”
If you are walking a dog that you are unfamiliar with, or you are concerned about the welfare of your own pets during Covid-19, then the Canine and Feline Sector Group (an umbrella organisation for animal charities) has produced more extensive guidance.
See here for details.