For just me and DH ... around £70 a week.. Kids left home several years ago, but we do keep some veggie and vegan stuff in for them for their visits 2 or 3 times a month... (I don't eat red meat, so enjoy veggie food too.)
Our £70 a week on shopping includes detergents, toiletries, smelly candles, etc, cat food (for 2 cats,) as well as food/general consumables (milk, coffee, bread etc,) and a bottle of wine for the weekend.
How people do it for £20 a week for a family just baffles me. Maybe it's because I am a lazy bum who isn't arsed with cooking from scratch and batch cooking all the time. 
Big deal. We don't smoke, we rarely go out for meals - maybe 4 or 5 times a year, we go the pub once a month (and spend £15 tops,) we don't have a gym membership, (or anything similar,) I don't spend £22 every 3 weeks on false nails, or £20 a time on a fake tan, I rarely buy beauty products or make up, I spend £20 a time at the hairdressers every 3 months, and I rarely buy new clothes. Also, we have a 10 y.o. car that was paid for 7 years ago.
I know plenty of people who spend lots of money on gym memberships, new nails every month, fake tans, new clothes every other week, tennis and badminton club memberships (and similar,) who smoke, who have a new car that costs them £200 a month just for the repayments (not including the insurance and tax and petrol!) and who spend £50 a month on their phone contract. Yet they smugly announce they only spend £17 a week on food for a family of 3 or 4, (and 3 'hangry' animals.)
I am sure a few people will come on here soon claiming they spend on NOTHING that I have mentioned. Not sure I will believe them though. 
Always find it bizarre that people post threads like this though. As if £35 is a lot for a weekly shop. It's like 'AIBU to feed my children fruit and veg, and generally healthy stuff?' And I don't understand why people need to seek validation from random strangers on the internet. Just buy what you need, when you need it/want it, and to hell with what anyone else thinks!