Hello,
As shown in the attached picture the two pulleys aren't function correctly when in the small-small chain combo. There is no gap between the chain and the jockey pulley as the chain passes through the tension pulley. When the chain is in the large-small combo the chain is spaced enough not to be a problem although I think isn't not good. What possible problems could be at the source? I'm guessing there's possibly something not right about the springs however when trying to inspect I can see nothing apparently wrong.

Chain is too long. You need to take some links out. Do a search on sizing a chain.

+1 I agree. is the bolt that holds the derailleur claw missing?

remove 2 links of the chain and you should be fine.

What everyone else said.

I doubt OP knows what constitutes 2 links nor how to properly remove them. Ditto on a simple search for sizing bicycle chain - check Sheldon Brown's site. No point in reinventing the wheel.

Yes, please don't remove an arbitrary number of links. Try Sheldon's method: https://sheldonbrown.com/derailer-adjustment.html#chain

It will give you the shortest chain possible to still allow you to run big/big. After sizing, if you still have the problem, then you are exceeding the rear derailleurs chain-wrap capacity and you will simply not be able to use the smallest chainring and the smallest cog or two combo(s).

The other option is to shorten the chain more to allow you to use small/small. The risk is that since the chain is shorter, if you were ever to shift into the largest chainring and largest cog or two or three, the chain or something else may break.

I have previously looked over Sheldon's many articles. I'll now re-read the specific section.
Yes I would think the derallieur claw bolt is attached.
An additional factor is that this bike has been used for sometime and this problem has just become more apparent. Possibly it wasn't so noticeable previous. A need to reduce the number of links suggests that when the bike was original assembled, several years ago now by a department store, the correct chain length wasn't installed. Does this support the suggested solution?

Not sure if this matters too much (the answers above will correct your 'gap issue'), but it does look like your jockey pulleys need replacement. Those are pretty pointy teeth there. And if you have a triple crankset, I believe the small/small combo isn't recommended due to cross-chaining. Anywho, If possible, check out the LBS or local bike co-op for a cheap rear derailleur replacement. That would be a better idea than replacing the jockey pulleys.