Anna7 is right, quarantine regs are stricter than lockdown was. You are allowed to buy basic essentials on your way hone if there is no alternative, but thereafter you will have to find someone to walk your dog and do your shopping - or else do it online. (Fortunately slots are now very easy to find, I booked last night for an Ocado delivery coming today between 7 and 8.)
From the DT
Self-isolating means remaining at home or the place you are staying – and not leaving it. So, you cannot go shopping or meet friends, and any exercise must be in your own home or garden. People can be fined £100 for failing to fill in a contact form with details of where they are staying. One in five will be called or texted to check they are following the rules. People who do not self-isolate can be fined up to £1,000 in England, Wales and Northern Ireland, and £480 in Scotland. There are fines of up to £5,000 for persistent offenders.