Have you tried Firefox browser?
I have never had a problem connecting to https://www.national-lottery.co.uk/
After the draw had taken place last night I was able to log into the site in my usual browser, and again this morning it is working. As this has happened several times over the past two weeks I am totally perplexed.
Not sure if this is the same issue. I could not access the lottery app from my iPhone unless I used wifi. Once I switched off parental control within my virgin media mobile account all ok after that.
Thank you. I did that but it still didn't work and I really wanted the parental control on, so I added it as a permitted site and then it worked.