The problem as you call it, wouldn't probably exist if the Portuguese people and police had not been denigrated so repeatedly in the UK press and those others criticizing them.
Perhaps a wholesale apology to Portugal might facilitate their help rather than repeated criticism.
Xenophobic elements of the UK tabloid press
did criticise the PT handling of the case.
There is also often fierce criticism of the UK police in the UK press. This often happens in established democracies.
Criticism from a foreign press may have led to a defensive attitude in Portugal... but how did all the "leaks ", many of which later appeared to be incorrect, appear in PT tabloids in a country in which there was judicial secrecy and a makeshift press officer?
Many of the UK tabloids relied on the PT tabloids for their "news". The Leveson inquiry is interesting in this respect.
How on earth Lizzy Spielberg keeps spouting press inventions as troooo facts is beyond me.