ロシアは、イギリスの事件とは何も関係がないと言っていて、これからどうするか決めると言っています。
Russia says that they have no connection to the incident in the UK, and say they are deciding what to do next.
I can't understand the function of 何も in this sentence. I'm sure that I'm wrong, but it doesn't seem to be needed to me. I can't fit it into the sentence grammatically, or give it a useful meaning.
I wonder if it's the same as in this answer. If so then please close as duplicate.
「ロシアは、イギリスの事件{じけん}とは何{なに}も関係{かんけい}がないと言{い}っていて、これからどうするか決{き}めると言っています。」
「何も」 when used in conjunction with a negative expression (「ない」 in this case) simply means "not anything" or "nothing".
This 「何も」 is completely different from the 「何も」 in the other question that you linked to. This one is pronounced 「なにも{LHH}」 and the other, 「なにも{HLL}」
The function of this 「何も」 is to mainly emphasize the following phrase 「関係がない」. An English equivalent would be "Nothing vs. absolutely nothing". Both mean "zilch", but you do use the latter quite frequently as well.
"Russia says that it has absolutely nothing to do with the incident in England and ~~~."
Other examples:
「やった～！今日{きょう}は何も宿題{しゅくだい}がない。」= "Yay! There is (absolutely) no homework today."
「このレストランには何もおいしいものがない。」 = "There is (absolutely) nothing yummy in this restaurant."