We're avoiding all UPF-type additives and went vegan last year and tbh it's a PITA.
The huge shock has been that 'natural' or organic or otherwise 'posh' ready made food has just as many UPF gums, stabilisers, emulsifiers, mono- and tri-diglyceride shite and preservatives than the bog-standard stuff we used to get. Most 'sourdough' bread from supermarkets is made with the Chorleywood method so is still very processed. Even posh wraps are full of shit (apart from Crosta and Mollica). So we couldn't even throw money at the problem if we had it 
But the longer I've been doing it, the quicker both the shopping and the cooking gets. Haven't fully solved the 'getting buy-in from teenagers' thing yet though ...
Pasta sauces are definitely the way to go for speed during the week. Some variation on a slow-cooked tomato sauce (v easy to batch cook and freeze) or a garlic, cream and mushroom one (we use silken tofu instead of cream).
When we weren't vegan, a pack of supermarket prawns and loads of garlic, chilli and olive oil plus chopped parsley was amazing with pasta.
There's an amazing 20 minute dhal recipe in the Spicebox book - I can post if you're interested.
Lots of recipes need onions to be softened/caramelised so i often double the amount and freeze half - that saves 10 mins the next time.
Sometimes it's easiest to do really basic 'English' stuff with good ingredients - again, if you're not vegan, things like egg and chips or beans on toast.
We use brown basmati rice (much less heavy than standard brown) and we always make double or triple and have it in the fridge to microwave for a quick carb, or turn into fried rice with garlic, spring onions, sesame oil and soy sauce or a cheats mujadara with caramelised onions from the freezer,some olive oil, salt and a tin of green lentils. Delicious.
In terms of ready-made food - Crosta and Mollica do great wraps but also pizzas and pasta which are comparable with other branded ready-mades like Pizza Express.
We are on a tight budget too and I have found Mr Organic's range of 'posh' tinned beans to be briliant - Greek-style beans, Italian-style, etc etc. No nasties, pretty tasty especially if you add some fresh herbs and vegan parmesan, and around £2.25 per tin. Non-vegans could add a bit of chorizo and grated cheese plus crusty bread for a genuinely satisfying £2 per head meal?
Tinned beans generally are a godsend - butterbeans and chorizo into your batch-cooked tomato sauce with some frozen 'mediterranean grilled veg'; kidney beans and soya mince plus Gran Luchito chipotle paste in the same sauce for chilli, etc etc.