Yes, do it! We have been very basic since September - partly as an experiment to see if we could, and partly because we really need to save a bit more money!
I do my meal plan every Wednesday & do a shop at Aldi every Thursday. What doesn't get purchased at Aldi doesn't get purchased, unless they've randomly run out of milk, bread etc. In the main shop, I include one "thing" each for the DCs - so that might be some chocolate for the younger ones & cider for DS1 (he's 18) but only a small amount. I also get some beer for DH for a Friday night & one bottle of wine or fake Baileys (£3.99) for myself. The only thing we would top up shop for would be absolute essentials like milk.
We are not buying anything we don't actually need, which includes clothes. We would have liked new winter coats (myself & DH) but have had our old ones cleaned instead. They may not be fabulous, but they'll keep us warm.
I've also had a big eBaying session, getting rid of clothes that people have either outgrown or that have gone unworn for so long that no-one's going to miss them now!
Other changes we've made are small like before I would have thought nothing of buying a drink while out (Diet Coke, coffee etc.), but now I'll wait until I'm home unless I literally can't wait. £2 here and £2 there adds up.
So far, it's been really successful. The DCs have had a few tantrums about wanting things (non-essential stuff like a DVD or something to do with the PS4 - points or games or what not) but overall have accepted it and despite having had a lower income for the past few months, I actually have quite a bit more in my account than I normally would 5 days before DH's payday! Not thousands or anything, but a few hundreds.