The SG embassy in London’s solution is not an option. They are
able to to issue an emergency travel document for entry to
Singapore only, but issuance is subject to submission of travel
itinerary, which would show that Singapore is not the first
destination (entry would be on the UK passport, which they cannot
know about).
I am calling ICA in Changi airport regularly, on 6
numbers advertised on their website, but not one of them is picking
up, hence my asking the question here. There is no need to reply if
you have nothing of value to add, or are unable to understand the
situation described.

do you still want Singapore citizenship? read
this.