So I'd start with increasing the amount of vegetables you eat. Whatever diet you choose, eating more veg isn't going to be against it unless you're going for the really wacky ones. The general rule of thumb is green veg to simmer in boiling water for c. 5 minutes. Most green veg is pretty much the same. I cook cabbage, asparagus and brussels sprouts differently but that's more personal preference. Carrots, c. 12 minutes. People swear by steaming instead, I don't think it makes much difference. Frozen vegetables like peas, broad beans, edamame beans and sweetcorn all work well and just need to be brought to a boil for 1-2 mins. Other frozen veg (apart from chopped spinach I'd add to curries) I don't think work very well as they tend to be a bit soft whatever you do.
With vegetables, I think it's a combination of not overcooking them and finding ones you like. When my son was little, if he didn't like something, I'd offer it again but perhaps cooked slightly differently. So even I as an adult swear that carrot batons taste better than sliced carrots. 😂
So start simple. If you are having a low calorie ready meal, say, then cook some vegetables to go with it so it really fills you up. Or get something like a yellow fin sole fillet from Lidl, they sell them coated with breadcrumbs in the frozen section. They're pretty tasty and at less than 200 calories each, with some cooked broccoli, cauliflower, peas, you'd have a really low calorie but filling meal.
Then also think about fruit. Again only bonkers diets ban it. The apple season last year was brilliant so even stored British apples are doing well and cheap. Grapes you can get pretty cheaply and strawberries are just coming into UK season. If you feel peckish, eat fruit.