Well - after all my hassling - I was told they won't issue a non-chip card - I can go and get a backup non-chip debit card linked to my credit card for backup 
After complaining, and requesting a new banker (yet again) to the "Manager Client Relations" - I got a response from her saying that my banker misunderstood and thought I wanted a new chip card. I asked for an explanation as to how she got confused by these two emails:
04 March:
"Could you point me in the right direction – I’m having issues with
this chip credit card of mine. Quite often it says “TRANSACTION
DECLINED” immediately after putting in my pin. Today I struggled for
almost 20min – before giving the woman my old card with the damaged
strip, which I only had on me by chance, thankfully it went through
after a few swipes.
I’ve had this at about four different retailers now – these times I’ve
resorted to using cash, thinking it was their machines – but I see it
doesn’t happen when xxxx uses her non-chip card.
It’s also not a pin issue…."
and then
05 March
"Further to the below, here is a copy of a declined transaction, its
getting embarrassing. 10 minutes later the card worked perfectly at
another retailer, then this morning it was declined again.
If there isn't an answer to this I'd like the card replaced with a
non-chip card."
After complaining, and requesting a new banker (yet again) to the "Manager Client Relations" - I got a response from her saying that my banker misunderstood and thought I wanted a new chip card. I asked for an explanation as to how she got confused by these two emails:
04 March:
"Could you point me in the right direction – I’m having issues with
this chip credit card of mine. Quite often it says “TRANSACTION
DECLINED” immediately after putting in my pin. Today I struggled for
almost 20min – before giving the woman my old card with the damaged
strip, which I only had on me by chance, thankfully it went through
after a few swipes.
I’ve had this at about four different retailers now – these times I’ve
resorted to using cash, thinking it was their machines – but I see it
doesn’t happen when xxxx uses her non-chip card.
It’s also not a pin issue…."
and then
05 March
"Further to the below, here is a copy of a declined transaction, its
getting embarrassing. 10 minutes later the card worked perfectly at
another retailer, then this morning it was declined again.
If there isn't an answer to this I'd like the card replaced with a
non-chip card."