I think it sounds like a lot of faff, because you have to log all your spending and be constantly mindful about which 'pot' you are spending from. Can you really be arsed updating it every time you buy a coffee? Although that alone might be enough to make you cut down 
In your situation, I'd have a really good look through your budget. Moneysaving Expert is good for this. There's also a weekly email, with various hints to make more of your money over time.
www.moneysavingexpert.com/family/money-help/
The demotivator is a good tool to show you how much your daily coffee adds up to over time.
Then get yourself five* accounts, either from your existing accounts, or open sufficient new ones so you have the following:
A main current account, that all your direct debits come out of. Do not spend from this account, but set up standing orders the day after payday or on a regular day each month (the 1st or the 28th would be a good choice) for the following purposes:
A savings account for annual and irregular expenses, eg Christmas, insurance, white goods replacement, holidays, car repairs, school uniforms, etc etc. Expect to pay quite a significant three figure sum into this account, unless you are on a very low income/don't have a car or spend much on holidays etc. These things add up, and could be where a lot of your money goes along with the coffees and pizzas.
Move another chunk of money from your current account each month to an account for food and petrol/travel and only buy these things from this account.
Also have a 'long term/big purchases' account for things like home improvements, car replacement etc, that you would hope to be able to pay for without borrowing, seeing as you are in a position with a good surplus on paper.
Finally, you get to your free spending account, which you fund with the amount of money that you want to spend on coffees, pizzas etc etc on a 'when it's gone, it's gone' basis. Only buy these things from this account. If you run out, you can't have it .
- You don't have to have 5 accounts, you might decide to combine the short and long term savings, you might decide to just buy your food and petrol from your bills account, although there's a risk of buying non essentials in the supermarket, so that would be something to watch.
But by doing the above, if you get into the mindset of only buying the non essentials using one particular card, you naturally limit these spends to the amount you put in this account, while knowing that money is put aside for essentials and other priorities like holidays etc.
You could possibly open accounts with Starling, Monzo etc, which is quick and easy through the apps, and you get different coloured cards, so can easily remember that the green Starling card is your spending card or whatever.