I'm, too, am not overly sure how Brexit enters into this.
Lots of Brits are fat quite simply because they gorge loads of processed rubbish containing excessive amounts of fat, salt and sugar. They do so not because they cannot afford to eat healthily (which everybody can) but because they cannot be bothered to.
Most unfortunately I have a McDonalds "restaurant" near me. It is a drive-thru (sic). The people who drive through it are predominantly overweight and they emerge with their purchases, ramming whatever it McDonalds sells down their face with one hand whilst steering with the other. The place sees a constant stream of couriers delivering the stuff to those who cannot even be bothered to fetch it themselves.
A household near me (couple plus three children) virtually lives on delivered food from various outlets. Barely a day passes without carrier bags full of the stuff being brought to the front door. All of the occupants are overweight, including their youngest child who can be no more than 8 or 9 years old.
People who feed themselves in this way simply cannot be bothered to feed themselves and their children properly. The article is quite right - many people in the UK see eating as simply a nuisance, to be endured with as little fuss or effort as possible, usually whilst they are doing something else of far greater importance. Until that changes (which is unlikely as the opportunities to eat conveniently seem to be increasing daily) there will always be large numbers of overweight people here.