OP, you poor thing. That sounds like hell on earth. You can't WFH and be sole carer to your kids. It just isn't possible. I bloody hate this country that so many women are put in this position.
There isnb;t a quick fix and it isn;t your or their fault, but I would sit them down at tea time tonight and say: we can;t survive like this. I have to work during the day. if I don't, I get no pay and we have no money for food, electricity, water etc,. We need me to work and I must have peace, that can't change. Then ask them how they think they can help. Ask how they think they can stay calm and quiet and entertain themselves during yoru work hours.
Set up a daily structure. It will feel tough at first but once you get into it, it will be easier because part of them pestering you is their sensing that you hate this life and that will unsettle them. they'll keep checking you;re still there for them. Ifyou give them loads of attention when you can, they might settle down in between.
Also set each of them up with a cosy place in different parts of the house - with a cushion/rug, cuddly toy, drink, book etc. if they fight , you send each of them to their cosy place to calm down. Not a punishment - a self-rehgulator. Say to stay there intil they feel calm then back to playing when they are ready. get them to be in charge of managing their own emotions.
Try an dstructure the day so it starts with some focused attentuion from you. Maybe get up early and do some exercise together, Anything from Joe Wicks to a walk or silly dancing in the kitchen. Get them to take turns to choose what they want to do as the morning fitness. Then have a healthy breakfast together - no sugar or refined carbs as that will get them hyper and fighting. Maybe wholemeal toast with peanut butter or an egg and soldiers.
After that, explain you need to work, Lay out some healthy snacks for them, and set them up with some stuff to do - a long film to watch, a not too messy craft project.
If you can, try to work for 50 mins each hour and come out to check on them for ten minutes. Give lots of praise for them being good.
Meet up again at lunch. Chat about what they got up to. Reward them for good behaviour. Mine loved a big pasta shell each in a jar if they had been calm. Once the jar filled, they'd earned a day trip.
At the end of your working day, greet them with cuddles as if you had been out of the home and missed them. Do something together - something summery - get the paddling pool out or find an ice cream van or BBQ some sausages - so they recognise you love being with them when you can.
This sort of plan doesn't always work smoothly but ime, when children are whiny and clingy and refuse to let you work it's one of three things:
they know you are stressed by them and so are on hyper alert to keep you in sight all the time - a sort of animal instinct against neglect
or they are so fuelled by sugar etc they can't behave well
or they are ill.
You can try and change the first two. Not easy but might help. The cosy corner thing really helped me with SEN children fighting as they just had to go and play alone until they were ready to play nicely together. I used to hear them start to pick fights and then whisper - stop or she;ll make us go in different rooms. It really does teach them to self-regulate squabbles.