Meaning: Very fit.

The allusion to a butcher’s dog is to a dog that would be expected to be very well fed from scraps. Why that is considered to epitomize fitness isn’t clear, as it might be thought more likely that the dog would be overweight than fit [no comment – Owl]. John Camden Hotten, in A Dictionary of Modern Slang, Cant and Vulgar Words, 1859, defined ‘butcher’s dog’ this way:

“To be like a butcher’s dog, that is, lie by the beef without touching it; a simile often applicable to married men.”

That’s clearly a different meaning, that is, butcher’s dog was then a metaphor for ‘something we are close to but cannot have’. That meaning has gone out of use. [Or perhaps not? – Owl]

Gary Martin www.phrases.org.uk 

Since this post is still viewed on a daily basis Owl feels the need to add the context.

The phrase was used by Boris Johnson whist self-isolating after he had been in contact with an MP who had tested positive for Covid in November 2020. Johnson had been hospitalised with Covid in early April.