Theresa May is to complete a trip to the Middle East by setting out her post-Brexit vision for the UK’s role in the region in a major speech in Jordan, outlining both UK efforts to combat Islamic State and wider, long-term help on economic and social reforms.

The prime minister is due to address an audience including Jordan’s prime minister, Hani al-Mulki, and much of his cabinet, at the end of a three-day visit that also saw her hold talks in Saudi Arabia on Yemen and make a surprise visit to Iraq. In talks in Baghdad on Wednesday, May spoke to the Iraqi prime minister, Haider al-Abadi, about the recapture of Mosul from Isis fighters, also meeting UK troops who had trained Iraqi forces who took part in the battle.

May is expected to highlight the threat posed by dispersing Isis fighters, some of whom have massed near the north of Jordan. There is also the risk of more returning to Britain – government figures estimate that around 850 UK-linked people of national security concern have travelled to the region to fight, with just under half having returned so far.

The prime minister is due to cover this threat in a part of the speech dealing with more direct security assistance in the region, also including training for Iraqi forces to clear Mosul and Raqqa of explosive devices left by Isis as it fled, and more security assistance for Jordan.

Jordan is seen by the UK as a vital bulwark in the region, but it is struggling with the impact of many thousands of Syrian refugees as well as high youth unemployment in a country where half the population is aged 24 or less.

May will also announce efforts to help the Jordanian economy in the longer term, including £60m in new grants, especially connected to education. The speech will also focus on regular regional targets for May. She will stress that peace in Syria can only realistically happen without Bashar al-Assad in charge, and note what the UK believes are Iran’s efforts to destabilise the Middle East.

Part of the Iran question centres on one of the most pressing issues she has faced on the trip – the deteriorating humanitarian situation in Yemen, where Saudi Arabia, which backs one side of a brutal civil war, is blockading the main airport and the port of Hodeida.

Saudi Arabia argues it must do so to avoid weapons reaching the Iran-backed Houthi rebels, who the Saudis claim have targeted rockets from Yemen to their country.

May met Saudi Arabia’s King Salman and the crown prince, Mohamed bin Salman, in Riyadh late on Wednesday after leaving Iraq. A Downing Street spokesman said that while May “noted that we shared Saudi Arabia’s concerns about Iran’s destabilising regional behaviour” she made it clear that aid and commercial supplies to Yemen must be restored “if we are to avert a humanitarian catastrophe”.

He said: “They agreed that steps needed to be taken as a matter of urgency to address this and that they would take forward more detailed discussions on how this could be achieved.”

May also discussed internal reform efforts with the Saudi crown prince, and it is understood British officials view his efforts as serious and zealous, in a country which has long promised changes that were never delivered. It is also understood that the message on reopening Yemen’s supply links was understood by Bin Salman.