The Queen will use her Christmas message to say 2019 has been “quite bumpy”, after she was drawn into a constitutional crisis by Boris Johnson and Prince Andrew was forced to withdraw from public life over his friendship with the sex offender Jeffrey Epstein.

The pre-recorded message is also sprinkled with what could be interpreted as references to Brexit, as the Queen urges a nation divided over Europe to “put past difference behind us” and “honour the freedom and democracy” won in the second world war.

Citing the example of Jesus, the Queen will say “how small steps taken in faith and in hope can overcome long-held differences”.

She will add: “The path, of course, is not always smooth, and may at times this year have felt quite bumpy.”

The Queen does not spell out what she means by “bumpy” but it comes after an unusually difficult year for the royal family.

In September, the prime minister inveigled the Queen into what was later ruled to be unlawful enterprise by proroguing parliament for five weeks at the height of the Brexit crisis. Opposition leaders warned that royal prerogative was being set against the will of the House of Commons, before prorogation was annulled by the supreme court.

In November, the royal family’s reputation was tarnished by a disastrous Newsnight interview the Duke of York gave about his friendship with Epstein. The prince’s lack of contrition and his failure to acknowledge Epstein’s victims prompted widespread criticism that forced him to step down from royal duties.

The royal year began badly when the Duke of Edinburgh was widely criticised for his involvement in a car crash and his initial failure to apologise to two people injured. It ended with the 98-year-old duke in hospital and potentially missing the family Christmas at Sandringham.

After the public relations success of the royal wedding in 2018, the public and press affection for Harry and Meghan also turned sour this year. The couple were criticised for their use of private jets while speaking out on environmental issues. The Duke and Duchess of Sussex also complained about press intrusion and were dogged by repeated speculation about a rift with the Duke and Duchess of Cambridge.

The Queen’s acknowledgment of a “bumpy” year will draw comparisons with 1992, which she less euphemistically described as her “annus horribilis”. In that year, the marriages of three of her children collapsed and Windsor Castle was damaged in a fire.

The Sussexes’ Christmas card. Photograph: @SussexRoyal/PA

This year’s message was recorded in the restored castle’s drawing room after the election but before Prince Philip was admitted to hospital for treatment for a pre-existing but undisclosed condition.

Prince Charles was asked about his father as he toured the flood-hit village of Fishlake in South Yorkshire on Monday. He said: “He’s being looked after very well in hospital. At the moment that’s all we know.”

In one passage of the message, the Queen reflects on the ceremonies she attended to mark the 75th anniversary of the D-day landings alongside other world leaders including the US president, Donald Trump, the German chancellor, Angela Merkel, and the French president, Emmanuel Macron.

Her remarks on this will be seen in the context of divisions over Brexit.

She will say: “For the 75th anniversary of that decisive battle, in a true spirit of reconciliation, those who had formerly been sworn enemies came together in friendly commemorations either side of the Channel, putting past differences behind them.”

She will add: “By being willing to put past differences behind us and move forward together, we honour the freedom and democracy once won for us at so great a cost.”

The Queen is filmed sitting at a desk featuring photographs of her family. One picture shows the Duke and Duchess of Cambridge and their children – Prince George, Princess Charlotte and Prince Louis – in an image used for the couple’s Christmas card. There is no photograph of the Duke and Duchess of Sussex, who are spending Christmas in Canada.

Other family photographs that can been seen on the desk include the picture of the Prince of Wales and Duchess of Cornwall that marked the 50th anniversary of Charles being invested as the Prince of Wales. There is also a black and white image of the Queen’s father, King George VI, sending a message of hope and reassurance to the British people in 1944.