What King Charles really thought about Sydney Opera House light display revealed

and before travelling to Admiralty House for an informal cup of tea with prime minister Anthony Albanese.

They saw the as they travelled through the city and are understood to have been deeply touched by such a wonderful gesture. They were also grateful for the warm welcome they received, despite the treacherous weather.

Shortly after arriving at Admiralty House they went out into the garden to take in the view and posed for a photograph before heading back inside.

The King and Queen had no engagements on Saturday, and enjoyed a "down day" to help them acclimatise to the punishing time difference and recover from their long-haul flight.

On Sunday their tour of Australia gets underway with 24 engagements between them over three days.

They will attend a church service at St Thomas' Anglican Church, North Sydney, in the morning with members of the public invited to meet the King and Queen outside the church at the conclusion of the service.

Locals have been advised to gather on the lawns next to St Thomas' where the weather forecast promises sunshine and temperatures of 20C.

Charles, 75, will then attend an event to celebrate the bicentenary of the legislative council. He will make some brief remarks and present a gift to mark the special occasion. The King will then hold two audiences at Admiralty House.

It comes as it is revealed that the monarch has made a significant personal donation to an "important new initiative" that aims to create opportunity and tackle contemporary challenges, including climate change and inequality in Commonwealth countries.

The Association of Commonwealth Universities (ACU) has launched today the King's Commonwealth Fellowship Programme that will offer fellowships to mid-career professionals, undergraduate scholarships and PhDs to candidates based in Small Island Developing States (SIDS). It aims to deliver short, medium and long-term impact for these countries and their communities.

King Charles hailed the fellowship and said: "I am delighted to support this important new initiative. Throughout my life I have believed in the power of education to improve lives and unite communities across the Commonwealth and beyond.

"There is so much we can learn from one another as we work together within the Commonwealth to tackle the major challenges of our age and, as these Fellowships do in Small Island Developing States, to address them where they are felt most acutely.

"It is my fervent hope that these new Fellowships will play a significant role in furthering the free exchange of knowledge and advancing the spirit of mutual support that lies at the heart of our Commonwealth - today, tomorrow and towards a brighter future for all."

The Fellowship Programme builds on two previous scholarship initiatives, demonstrating His Majesty's long-term commitment in this area and his desire to increase opportunity.

It aims to strengthen climate resilience, build capacity in education, health and engineering, and develop resilient public services and the skills of those who support them.

This prestigious programme will fully fund, train and support multiple cohorts of undergraduate, postgraduate and mid-career King's Fellows in its first few years and seeks to engage participants from every Commonwealth SIDS.

It will be tailored to the specific and unique needs of SIDS, but with broad thematic focus areas to facilitate knowledge sharing.

The fellowship has been launched in celebration of 75 years of the Commonwealth, and supports the theme of this year's Commonwealth Heads of Government Meeting (CHOGM) 'One Resilient Common Future: Transforming our Common Wealth'.

The King, as the Head of the Commonwealth and Patron of the ACU, will ceremonially launch the programme at CHOGM next week.

He and the Queen will travel to Samoa on Wednesday following their six-day tour of Australia.

On Monday, the royal couple will travel to Canberra where they will be officially welcomed to the country.

They will attend events at the Australian Parliament House, the Australian War Memorial and the National Botanic Gardens.

Separately, the King will visit CSIRO, the Commonwealth Scientific and Industrial Research Organisation, meeting firefighters and learning more about the centre's work to combat the bush fires which devastate millions of hectares of Australian land each year.

Meanwhile, the Queen will join a discussion on domestic and family violence, with some of those whose lives have been affected by it, and experts who work in the field. She will also meet representatives of GIVIT, a charity which matches donors with those in need, of which she is Patron.

The final day of engagements will take place back in Sydney, where Their Majesties' will attend a community BBQ in Western Sydney, sampling a range of produce from across NSW and experience the cultural diversity of Australian communities.

The King and Queen's visit will conclude with a visit to Sydney Opera House and a Fleet Review of the Royal Australian Navy.

On Wednesday the royal couple will fly to Samoa for another busy few days of engagements before they head back to London on Saturday.