I think the No Spend Days are about non essentials, like coffees, lunches or 'stuff' that you don't really need (clothes, bits from B&M or whatever you tend to buy that you could do without).
If that's what's derailing your budget or causing you to not be able to afford bills/food or the things and experiences you actually want, then it might be worth doing.
But probably more constructive is to review your budget, make sure you have money aside for emergencies and annual and irregular expenses like Christmas, insurance, car running costs, white goods replacement etc. Also that you're getting the best price on everything you buy and you're not wasting money on things you don't value like subscriptions you don't use.
When you do spend, do it mindfully and think about how to reduce the cost. For example if you went for a day out over the Easter Holidays, you could just go to an attraction, pay full price for entry and buy lunch for everyone in the cafe. Or you could look for a deal and book ahead, take a picnic and perhaps just buy an ice cream while you're there. And the day out will probably cost under half the amount doing it that way.
Or you could look for somewhere that you could visit regularly and does annual passes, which often cost hardly any more than a single entry ticket. Also look for other free or cheap things to do, lots of places like libraries or museums often have free events in the school holidays, so do as many of those as you can. The no spend aspect would be not automatically buying food and drink while you're out, so see if you can take it with you, or if you're only out for a few hours, just wait until you get home.