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Today's government coronavirus conference was led by Home Secretary Priti Patel, who was joined by Paul Lincoln, head of the UK's Border Force, and Sir Patrick Vallance, chief scientific adviser to the UK government.

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Key points to take away from today's speech are:

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• Home Secretary Priti Patel says 36,393 have died after contracting coronavirus in the UK - up 351 on yesterday. Some 140,497 tests were carried out yesterday, with 3,287 new confirmed cases.
  
  

• Home Secretary Priti Patel has announced that international travellers entering the UK will have to self-isolate for 14 days - bar some exemptions. The new measures will come into effect from 8 June.
  
  

• The home secretary says new arrivals could "potentially cause a second wave". "I know that families both at home and abroad are desperate to be reunited. But by taking these steps, we can save more lives," she said.
  
  

• Priti Patel says there will be a fixed-penalty fine of £1,000 for those who break the measures. There will be spot checks conducted by Border Force at the border. 
  
  

• Mr Lincoln says Border Force has stopped "thousands of counterfeit COVID-19 tests" from coming into the country, as well as counterfeit masks. It has also discovered other illegal items including an AK-47 rifle.
  
  

• "This is a peak we have managed to suppress by things we have all done," says UK chief scientific adviser Sir Patrick Vallance. "As some of the rules around this are relaxed, it's important we maintain social distancing."
  
  

  

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• Home Secretary Priti Patel says the government's advice remains the same that only essential travel is advised, after being asked about when people can book holidays.
  
  

• Priti Patel says the UK has been working closely with the French government. She said that some of the exemptions already listed, such as for hauliers, will affect France.
  
  

• Professor Vallance says we are now "much more positive" that those who have survived coronavirus produce an antibody response. However, he did say that we don't know long immunity from antibodies lasts for or how effective it is.
  
  

• Priti Patel has asked for a to pause to remember terror victims, three years on from the Manchester Arena attack and seven years from Lee Rigby's murder. "My thoughts and all our thoughts across the nation are with those who lost their loved ones and suffered on this incredibly difficult day," she said.

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To read a brief summary of last night's points and important measures click here.

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