Clingy 4 year old

[Tweenies12]

Just looking for a bit of advice really. My eldest DS who is 4 literally screams until he's sick if he cannot be in the same room as me. Today for instance, I'm not very well and DH kindly got up with the DC so I could rest. DS1 would not go downstairs for breaskfast with him and his younger brother, insisted on staying upstairs with me. When I tried to explain that I wasn't well and he could go down and watch some TV or whatever for a bit whilst I had a little rest he screamed and screamed. DH ended up carrying him down and he screamed for ages for me. DH has been very patient with this but I can tell its getting him down now.
DS is fine when I go to work and DH is looking after him and he gets 'boys day' and is always full of beans and chatty about his day when I return. But if I'm in the house I cannot go anywhere without him tagging along, can't shower, can't go to the toilet sometimes, can't run upstairs to grab something. Its becoming a nightmare.
What can we do? We've tried talking to him when he's calm, we've tried distracting with TV, games etc. Ive even tried being sturn with him and just completely ignoring it. But it's every single time i try to leave the room.
He does it with my parents too, will always want to come with me.

Any advice on what we could do to help him would be great.
Hope it makes sense too, I'm quite poorly today so feel as though I'm garbling.

Following with interest. My DS 3.5 is a bit like this at the moment, he’s ok if I’m out or he’s out with DH or his grandparents but can’t cope with being separated from me if I’m in the house/garden. Either he will follow me around or constantly ask DH “where’s mummy?” (When he knows I’m in the shower etc). Sometimes (usually if he’s tired/hungry) he will scream and cling to me begging for me to stay with him when I want to pop to the loo.

DS struggles with separation anxiety generally (nursery has been a challenge) so now it’s the holidays we have been doing lots of practice spending time with DH or GP. But I’m not sure what the solution is when we are all at home. I try to strike a balance - he can follow me upstairs but I won’t not go to the kitchen/bathroom etc. Sometimes I ask him to hold something for me while I go, or remind him what we can do when I’m back down. He also has a set of sand timers he really likes so sometimes we make a game of it using those. But those are all distractions rather than solutions.