The strength of the union is crucial to the success of the UK as it leaves the EU, Theresa May has told Scottish Conservatives gathered for their spring conference in Aberdeen on Friday afternoon.

Promising that a Conservative government “will always put the interests of our union first”, May – who did not mention her party’s council election losses – told delegates that the future for the whole of the UK was bright, “if we leave the EU with a deal that works for us”.

“We have everything it takes to make a success of what lies ahead of us,” she said. “The strength in diversity that comes from being a union of four great and proud nations will be crucial to that success.”

May welcomed the Scottish Conservative leader, Ruth Davidson, back from maternity leave and credited her for the dramatic rise in the party’s fortunes in recent years. May said Davidson showed that “success in one of the biggest jobs in British politics should be no barrier to a woman starting a family”. Davidson returned to frontline politics this week, six months after giving birth to a baby boy.

Reiterating her determination to honour the result of the EU referendum, May told the conference that “work continues” to secure cross-party support for a deal with Labour, “with one clear aim: to get a deal over the line in parliament”.

“That is the only way to deliver on the instruction of the British people,” she said. “And across the UK, people want to see the issue of Brexit resolved and for our country to move forward.”

Attacking the Scottish National party’s “obsession” with independence, she accused the SNP leader and Scottish first minister, Nicola Sturgeon, of having “no interest” in working with her to deliver a good Brexit deal for the UK.

May said: “I would have welcomed a first minister of Scotland who wanted to work with me to deliver a good Brexit deal for the UK. But I knew from the start that Nicola Sturgeon was not interested in that outcome. She saw Brexit as an opportunity to further her party’s obsession with one thing and one thing only: independence”.

Earlier in the afternoon, the home secretary, Sajid Javid, described the local election results as “disappointing” in his first speech to a Scottish Conservative conference, acknowledging: “We knew there was frustration about our national politics.”

Javid warned that the Conservatives were seen as “a divided team”, saying: “A divided party cannot unite a divided nation.” He added that this could usher a “socialist-separatist alliance” into Downing Street, saying: “Sturgeon will have [Corbyn] in her pocket, and I have no doubt he would readily pay her price: another independence referendum.”

Javid’s fellow cabinet minister Michael Gove will address the conference on Saturday, while former minister Esther McVey is appearing at a fringe meeting. Scottish Tory sources said a number of potential leadership candidates had been “discouraged” from attending the event, amid concerns that their appearance could distract from Davidson’s return.