The act of menu planning should lead to budgeting quite naturally. There are a couple of 'tricks' you can use to make it easier on yourself.
The first is a 'working backwards' way: basically, you look over your shopping receipt and decide from
that what you will be having for B/L/D ... crossing off the items on your shopping list as you "use them up" on your menu plan (cross out in pencil because, if you need to, you can still use that same shopping receipt to make up the next shopping "list"
A second way is also a "working backwards" way: don't plan ahead at all!
Simply write down what you *have* eaten that day on your family calendar/diary. In 7 days time ... you have a one week menu plan

In 28 days time, you have a 4 week menu plan (and if you stick at it all year, you not only have 52 weeks menu plan, but a "seasonal" one too

)
A third way is to make up a weekly menu plan based around the old fashioned idea of Monday will be a meal based on X; Tuesday will be a meal based on Y; Wednesday will be a meal based on Z (with X, Y, Z being the main ingredient)
For Example: Sunday will be a roast meal; Monday will be an egg meal; Tuesday will be a cold cuts (from Sunday roast) meal; Wednesday will be a hearty soup meal (based on leftovers from roast); Thursday will be a vegetarian meal; Friday will be a fish meal and Saturday will be a Fake-Away meal.
This is the easier to budget because a) your basic shopping list will remain the same; b) you barely have to think about what you are having (time saving) and c) it is based having a Roast and two other meals from it (so, that's half the week taken care of!)
Another example: Monday (eggs); Tuesday (cheese); Wednesday (mince); Thursday (beans/pulses); Friday (fish); Saturday (vegetarian); Sunday (chicken) Then, you look up as many *different* meals you could make with those main ingredients. E.g mince = bolognaise, shepards pie, meatloaf, fake kebab, homemade burgers etc. Straight away that is 5 different meals or, put another way, 5 weeks of Wednesday meals
Hopefully, there will be something in this post which will be of some use to you.
Wishing you luck in winning the budgeting/menu planning battle