Dear T S:

You wrote:
> I am writing the sentence,
> “Other political partys’ phoney words”

This does not exist. A singular possessive ends with an apostrophe before the s. The plural of party is parties.

> or
> “Other political parties’ phoney words”
> Which is correct?(UK English)

This is correct as long as you are talking about more than one party. It is the same on both sides of the pond.

See “Apostrophes Showing Possession” and “Plural Possessives” in Grammar Slammer or https://englishplus.com/grammar/00000131.htm and https://englishplus.com/grammar/00000132.htm for more on this.