uk – Do I have to quarantine and/or taken another PCR if I have been PCR-tested negative but been in contact with someone positve in the preceding days?

I am Italian and am fully vaccinated with Astrazeneca-Pfizer, and I came in England for two weeks. So I’m just a traveller and not an expatriate. However, based on the help center, I think this is the right place to ask the question. However, please, let me know if you think that Travel or Law are better places for asking this.

The following is the timeline of the events of my travel.

  • I took an antigenic test on Sunday, September the 5th, evening, and it resulted negative;

  • I flew from Italy to UK on Tuesday, September the 7th;

  • I took the 2nd day PCR test on Wednesday, September the 8th (the result of which I’ve received yesteday)

  • Yesteday, Friday September the 10th, I received an e-mail from NHS Test and Trace that informs me of the following

    (…) NHS Test and Trace has identified you as a contact of someone who has recently tested positive for COVID-19. You must now stay at home and self-isolate for 10 days from the date of your last contact with them, unless you are exempt. You should now visit your NHS Test and Trace account to provide personal details. You should do this even if you think you are exempt from self-isolation. This helps us to advise you on what you need to do as a contact and give you advice on how to protect your family, friends and local community. (…)

    and another e-mail from NHS which reads like this

    (…) You should book a PCR test to check if you have COVID-19, even if you do not have symptoms. Book your test at https://contact-tracing.phe.gov.uk/links/ask-for-a-coronavirus-test.

    Unless exempt, you must continue to self-isolate even if your test result is negative. This is because you might still become infectious. (…)

    so I have created the account and provided the required personal details as per the part in bold.

  • Yesterday, some time after that e-mail and after I had completed the above request, I have received the result of the day 2 and it is negative. Specifically, among other things, it contains this sentence:

    (…) Your coronavirus (COVID-19) test result is negative. You did not have the virus when the test was done. (…)

The above sentence, tells without doubt that I did not have the virus when the test was done, which is September the 8th, which means that I have not contracted the virus from the contact that NHS informed me about, because it was on September the 7th.

Therefore I think there should be enough evidence that there’s no reason for me to self-isolate or take another test.

However, since the I could be fined if the NHS thinks differently, I’m asking here to seek help in understanding my situation better.