As Keir Starmer fights for his political future in the wake of dismal results in elections in Scotland, Wales and English councils, Ms Rayner is a key Labour power broker.
She has not ruled out running in any Labour leadership contest but said she would not ‘trigger’ a contest herself.
If she does not stand as a candidate to succeed Sir Keir, Ms Rayner would still be expected to return to the top of government by being handed a senior role by other leadership hopefuls such as Andy Burnham or Wes Streeting.
She was recently reported to have rebuffed attempts by No10 to install her as Mr Streeting’s replacement as Health Secretary in Sir Keir’s administration.
Mr Streeting quit the Cabinet role after losing confidence in Sir Keir’s leadership, with a string of junior minister also resigning from the Government in the wake of Labour’s local elections meltdown.
A contest to replace Sir Keir appears to be on hold while Mr Burnham, the Greater Manchester mayor, seeks a return to Westminster at the Makerfield by-election.
It has been suggested, if he does see off a challenge by Reform UK to win the seat, Mr Burnham could be set for a ‘coronation’ as Labour’s new leader.
Ms Rayner and Mr Burnham held secret talks at her Greater Manchester constituency home in April.
But allies of Ms Rayner denied claims she had agreed a pact with Mr Burnham to support him for the leadership.
Ms Rayner has had an on-off relationship with left-winger Mr Tarry, the former Ilford South MP, following her separation from her husband.
She was one of tens of thousands of Brits who flocked to the coast and beauty spots to bask in the blistering heat despite official government guidance to stay out of the sun during the hottest times of the day.
Brits were seen lounging on Bournemouth beach in Dorset early on Bank Holiday Monday
The Met Office said the 34.8C heat is ‘exceptional in the UK even in mid summer, let alone in May’.
Wales saw its hottest ever temperature in May on Monday evening, with 32.2C recorded at Hawarden Airport in Flinshire. The previous record of 30.6C in Newport stood for 82 years.
Up to nine counties, including Greater London, Surrey, Norfolk and Oxfordshire, saw temperatures soar above 32C – and the Met Office forecasts the mercury could yet climb to 35C today and tomorrow.
Amber and yellow health alerts remain in place across England, as temperatures continue to soar on what the Met Office has described as an ‘unprecedented’ heatwave for this time of year.
The warnings came as a man died on the beach in Hastings, East Sussex, following a ‘medical incident’, and a 15-year-old boy drowned at Swanholme Lakes in Lincoln on Sunday.
Elsewhere, almost 60 people were treated for conditions including heat exhaustion at the Edinburgh Marathon on Sunday and around 500 properties supplied by South East Water, in Sussex and Kent, were hit with outages and low pressure.
On Monday, beaches across the country were full of sunseekers while others descended on lidos and parks as they made the most of the final day of a scorching weekend.
The record high temperature of 34.8C was recorded in Kew Gardens at around 4pm, beating the previous records of 34C at Heathrow Airport and Bushy Park, Teddington, earlier on Monday.
The previous hottest ever May day of 32.8C was recorded in Camden Square, north London, on May 22, 1922, and in Horsham, Tunbridge Wells and Regent’s Park on May 29, 1944.
In a record-breaking spell of hot weather, temperatures soared to 30.9C in Wales, 25.5C in Scotland and 24.6C in Northern Ireland.
Tomorrow is expected to be another extremely hot day, with a peak of 35C expected in London, the Home Counties and Cambridgeshire.
The blistering heat will continue through the week, with highs of 31C forecast for Wednesday, 30C on Thursday, 27C on Friday and 28C on Saturday.
Tom Morgan, a Met Office meteorologist, said: ‘We rarely see temperatures above 35C, even in the summer months, so to see temperatures getting close to 35C in May is, as I say, pretty historic.’
Grimsby Town and Salford City fans baked in the heat at Wembley as the two sides contested the League Two Play-off final
A wedding couple pose for pictures in the sunshine on Westminster Bridge in central London
Tourists were seen enjoying the conditions on Bank Holiday Monday on Westminster Bridge
People enjoy the hot weather on Primrose Hill, north London, as the UK has recorded its all-time hottest May temperature
Tourists shelter with an umbrella at an ice cream van on Westminster Bridge
The Met Office said the warm spell has been driven by the development of high pressure over the country that caused air to sink, compress and heat.
Scientists say the record-breaking heat is a stark reminder of how the climate crisis is impacting lives in the UK.
More heatwaves are expected across the summer due to the developing ‘super El Niño’.
The phenomenon, which supercharges weather events such as making heatwaves hotter, is predicted to hit in 2027 but it is expected to begin emerging this summer.