How to encourage independent play?

[Brookville]

I have two lively,energetic DCs aged 4 & 3. On the 3 weekdays when I'm with them (2.5 days at work) I'm worn ragged by their inability to get stuck into anything without me sitting with them.
I thought it was because they wanted more of my time so I'll always do an hour of arty stuff after breakfast and again after lunch, and we go to playground but they always want me to play hide & seek or push them on swings. If I take a breather on the bench they stop running about and whine!
At home we have Duplo, Happyland, cars etc but it's rarely used. They hang out of me even when I set it all up and start them off. All I want is to stick the washing on / clear up or even steal ten minutes on the sofa whilst they play around. Too much to ask?!
DS (older) is worse- not interested in playing with toys at all sadly so I struggle with him. I think he puts DD off them too. She's a bit more focussed on playing when he's away at nursery.

Why can't they help you? I put DD1 to work. She empties the washing machine, puts in a new load, presses the buttons etc. She stands on small stepladders and helps with dinner - transferring, peeling, etc. She helps set the table, empty the dishwasher, etc. She is 2.4 years old and I have 5 month old baby.

Thanks Stargirl, they do help but I'd like them to play and not always hang out of me. I appreciate young kids do follow you about but my 4yo I'm convinced could get stuck into something fun. He does s bit of drawing at times. But minimal!

You do far more with yours than I do! An hour of art after breakfast 3 days per week,wow! I think I've just neglected mine a bit more and let them get on with it .Not sure if this is good advice but if I need to do housework or washing I just do it and they either tag along and chat or more likely go and play on their own and sometimes together (they are now nearly 2,nearly 4 ,and 5)

Super you've got a tonne more work on your hands than me with 3 under 6 wow! I do try and get on but today here's what happened: went upstairs to put away a week's worth of clean laundry. DS snuck scissors into his room and pretended teddies were at the hairdresser.... Need I say more? Of course I had to intervene! He even cut a lock of his own hair and DD would've been next.

Or else DS hurts sister when my back is turned. Yawn.

I've found it better to do small things together instead of a long time with my 3 yo.

What I do is sit with her and get started on something, get the happy land out, get the little people having a birthday party etc or something. Set it up together and play and then once she's into it (usually after a few mins) leave her to it. Then do se thing after a while with something else, jigsaws etc.

I'm sure it was in the happiest toddler on the block book I read when she was little about these snippets of play together and I thought it was a good idea.