It's a bit of a chore. So here's how we split it because some people are blinded by snobbery about brands but some of the ones traditionally lower down the scale do have some worthwhile value for some types of food.
We prefer Iceland for frozen veg (not meat), Lidl for fresh vegetables (& fruit too mostly), but the default for everything else is Sainsburys due to convenience for us and it's a reasonable balance of price/value/quality for our wants. Occasionally Tesco gets a look-in, but we avoid certain food types in each because they don't do as good a job as others nearby.
One other note - our local Lidl recently refurbished and added a proper bakery (they had a single machine shoehorned along one wall before). We've discovered the jam doughnuts there are some of the best, fresher and fluffier than the posh Patisserie Valerie ones I occasionally buy for the team at work (though not quite as much jam) and way cheaper - 19p each!
We don't have an Asda or Waitrose close enough nearby that they'd get used regularly. We do have a relatively new Morrisons but we haven't frequented it often enough to discover whether there is something there it does better than most of the others. Comments welcomed!
If your town has these close or you do large/frequent enough shops for each type of grocery, then it's easier to split your shopping for these but I do understand the convenience of going to one place for everything.
Holland and Barrett is also good when they have sales on (eg. their Penny sale) for dried nuts, fruit, cereal bars and such (particularly the Nakd bars which we like, partly because they're lactose-free); but otherwise we order online or look out for other deals as they can be quite expensive when not on sale. The sales are quite regular though - stocking up on one can usually take you through to the next one for the higher usage items, so we only do a small part of our spend there at full price :)