It won’t change anything, as you say, but it would be controversial both domestically and internationally. For starters, politicians generally won’t say anything specific about even apolitical, uncontroversial crimes, in case they prejudice any future trials. Obviously, this is neither apolitical nor uncontroversial.
Also, it wouldn’t actually silence his critics on this, precisely because it won’t change anything. The war will continue, so people would just start demanding that he demand issuing arrest warrants for Israeli government ministers who come to the UK, or trade embargoes, or whatever.