The Welsh Conservative leader Darren Millar has told the first minister to “get on with the day job” instead of focusing on the prospect of independence at a speech on Sunday.

Darren Millar told the Conservative Party conference in Birmingham that “Britain needs Badenoch” and reaffirmed his party’s support for the UK.

It comes after First Minister Rhun ap Iorwerth called for a “new deal” for Wales from the UK government at a Plaid Cymru conference, and said at a rally there was “no turning back” on the independence journey.

Millar says his party is committed to keeping the UK together and that Britain’s legacy should be used to inspire future generations.

Millar returned to the expanded 96-member Welsh Parliament after May’s Senedd election with a group of seven Welsh Tory members – down nine on the previous parliament.

Polls at various points during the election campaign had suggested the party could face a wipe-out, in part because of the rise in popularity of Reform in Wales.

The Tories could nonetheless end up doing a deal to pass the Welsh government’s budget – its spending plans for the next financial year – after holding talks with Plaid, which is running a minority administration and needs to do a deal with another party.

Ahead of the speech on Sunday, the Tory shadow Welsh secretary told BBC Wales Plaid would need to consider lowering taxes if it wanted her party’s support.

Millar says the Welsh government must focus on fixing public services and defend the relationship between the four countries of the UK – saying his party “will never allow” the break up of the union.

“A plan to draw a slate curtain between Wales and the rest of the UK will cause more harm than good for our children and future generations,” he says.

He points to rising NHS waiting lists, claims Welsh businesses have “continued to struggle” since Plaid came to power, and that ap Iorwerth had instead decided to “cosy up to the SNP and Sinn Fein” referencing the recent meeting in Cardiff between the three countries leaders.

“He then signed a pact to promote the break-up of our United Kingdom,” he says.

“The whole jamboree was seized upon by Vladimir Putin’s foreign minister, Sergei Lavrov, who gleefully spoke up on Russian TV about the prospect of independence referendums across the UK.

“So my message to Rhun ap Iorweth today is this – get on with the day job.”

Referencing ap Iorwerth, Millar says: “He told voters in May that the Senedd election was not about independence.

“Well, either he didn’t get his own memo or he deliberately chose to deceive people.

“Because just like the Pied Piper of Hamelin, the Plaid Piper of Anglesey has tried to hoodwink people.”

Miller describes the UK as “more than a political arrangement”, saying each helped to develop industries, abolish the slave trade, liberate Europe, and shape the modern world.

“We are a shared family of nations. For centuries, the people of Wales, England, Scotland and Northern Ireland have lived together, worked together, and traded together.

“Of course, there are those on the left who say we should apologise or be embarrassed about our history.

“But I say that it is a legacy and a heritage that we should be proud of and use to inspire the next generation.”

The Shadow Welsh Secretary branded a recent meeting of the first ministers of Wales, Scotland and Northern Ireland a “separatist summit”.

Mims Davies was speaking at a discussion on the union at Conservative party conference in Birmingham.

She also claimed the Plaid Cymru Welsh government could not afford its flagship childcare policy.

“That has meant that families have been sold a pup,” said Davies.

“It feels that if you’re living in Wales, life is far too hard, and there is nobody really standing up for the people of Wales,” the MP told delegates.