I prefer the Book of Divine Worship, Rite One. (Anglican Use of the Roman Rite)

The ICEL Text that I can find, is just atrocious as a latin translation. If I wrote a translation of the latin text and handed it to my latin teacher, I am sure she'd give me about a 5/10 for it, and mostly because it conveys most of the ideas, even if it doesn't express the grammar or have any real artistic merit.

You are God: we praise you;
You are the Lord: we acclaim you;
You are the eternal Father:
All creation worships you.

To you all angels, all the powers of heaven,
Cherubim and Seraphim, sing in endless praise:
Holy, holy, holy: Lord, God of power and might,
heaven and earth are full of your glory.

The glorious company of apostles praise you.
The noble fellowship of martyrs praise you.
The white robed army of prophets praise you.

Throughout the world the holy Church acclaims you:
Father, of majesty unbounded,
your true and only Son, worthy of all worship,
and the Holy Spirit, advocate and guide.

You, Christ are the king of glory,
the eternal Son of the Father.

When you became man to set us free
you did not spurn the virgin's womb.

You overcame the sting of death,
and opened the kingdom of heaven to all believers.

You are seated at God's right hand in glory.
We believe that you will come, and be our judge.

Come then, Lord, and help your people, bought with the price of your own blood, and bring us with your saintsto glory everlasting.

V. Save your people, Lord, and bless your inheritance.
R. Govern and uphold them now and always.
V. Day by day we bless you.
R. We praise your name for ever.
V. Keep us today, Lord, from all sin.
R. Have mercy on us, Lord, have mercy.
V. Lord, show us your love and mercy;
R. for we put our trust in you.
V. In you, Lord, is our hope:
R. and we shall never hope in vain.

BDW and rite one BCP are indeed the same.
Interesting question: is it licit to use texts of other Catholic rites or uses in normal Roman rite situations when this might result in a significant improvement of text and/or music?

Plus: it seems to me that I was told decades ago that it was licit to use older translations that were not the current official ones if they were wedded to historic music. Can anyone verify this? This would mean that one could sing the Willan ordinary in a Roman parish if he or she wished. I HAVE heard of quite a few Roman parishes who use The Hymnal 1940.

And Te Deum, by the way, is set to several Anglican chants in the 1940, as well as several psalm tone versions. I've seen few to no English adaptations of the original Gregorian music that were pleasing to any degree. Paul Ford's in Flowing Waters comes close (close!).

Are any of you contemplating singing a solemn Te Deum after the dismissal at mass on Trinity Sunday? We will at Walsingham. Lots of smoke throwing (in complete circular rotations), then the versicles and responses and collect.

I'm assuming that the question is really about what translations of the Te Deum are approved for the Office of Readings. I'm also putting together an Office of Readings service in which I need to use the Te Deum.

I'd imagine that will involve a new translation of the Te Deum as well.

I'd imagine that a new translation of the Te Deum will mean a new Te-dium for composers and arrangers as well.

Personally, I have always been partial to the BDW/BCP (Rite One) translation ... it has a venerable history of excellent musical settings, as well.

The stanza that is also found in the Sanctus is particularly awkward after now having been accustomed to the corrected translation in the Missal for the past 5 years:
Holy, holy, holy Lord, God of power and might.
Holy, holy, holy Lord God of hosts.

References:
http://www.ccwatershed.org/blog/2016/feb/7/phrasing-sanctus/
http://www.adoremus.org/0602Sanctus.html