I have been unable to find any direct information as to whether the New Testament Bible in Basic English used the 'Received' or the 'Critical' text.
What I have found are a few sample texts from the N.T. Bible in Basic English, that may provide some clues:
John 1:1, 14
1 From the first he was the Word, and the Word was in relation with God and was God. ... 14 And so the Word became flesh and took a place among us for a time; and we saw his glory—such glory as is given to an only son by his father—saw it to be true and full of grace.
For God had such love for the world that he gave his only Son, so that whoever has faith in him may not come to destruction but have eternal life.
"Jesus said to them, ‘Truly I say to you, Before Abraham came into being, I am.’”
8 Because by grace you have salvation through faith; and that not of yourselves: it is given by God: 9 Not by works, so that no man may take glory to himself.
Looking for the glad hope, the revelation of the glory of our great God and Saviour Jesus Christ;
From About the The Bible in Basic English I have ascertained that the Bible in Basic English appears to be based on the Authorised and Revised Versions of the English Bible.
The King James (or Authorised) New Testament was translated from the Textus Receptus (Received Text) series of Greek texts.