Police officers separated the two groups into pens and took away at least two protesters following scuffles and chanting by both sides, according to an AFP photographer.
"At around midday a number of demonstrators made their way out of both pens and onto Whitehall, briefly blocking the road," police said in a statement.
"A small number of protestors were arrested for a variety of offences including obstruction, assault and criminal damage to a motor vehicle," it added.
"Arrest Netanyahu" and "war criminal" they chanted, some holding up posters calling for an end to the blockade on Gaza as well as images of the Israeli leader plastered with the words "child killer".
Also Read
Others waved flags, including at least two from Lebanon's Shiite movement, Hezbollah.
Facing them were around 100 pro-Israeli demonstrators, many waving the Israeli flag.
The protests ended at around 2.30pm (1330 GMT), according to police.
More than 108,000 people have signed a petition urging the arrest of Netanyahu for war crimes, enough for the issue to be considered for debate in Britain's parliament.
In 2014, Israel and Hamas militants fought a 50-day war in Gaza which left more than 2,251 Palestinians dead, most of them civilians, and 73 on the Israeli side, most of them soldiers.
Britain is pushing for a two-state solution to resolve the Israeli-Palestinian conflict and "will reinforce this message to Netanyahu during his visit," according to an official response to the petition.
Netanyahu's office declined say what would be on the agenda for the talks, although the topic of West Bank settlements is likely to come up.
Israel is also deeply concerned by July's nuclear deal between Iran and major powers -- including Britain.
Netanyahu will return to Israel on Friday.