Chat about Novel Coronavirus - 2019-nCoV - COVID-19

But I found I continued to test positive on a pcr test for a month after having it, it's just you aren't contagious.

Thanks to the ONS study they know that some people can continue to test positive on a PCR test for up to 90 days after having it.

It's why the gov.uk 'get a pcr test' website (https://www.gov.uk/get-coronavirus-test) says not to get a test if you've had a positive test recently:-

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You should not use this service if you’ve received a positive PCR test result in the last 90 days, unless you develop any new symptoms.
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The ONS study is partially responsible for this:-

https://www.ons.gov.uk/surveys/informationforhouseholdsandindividuals/householdandindividualsurveys/covid19infectionsurveycis/howyourresultswillbeused

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From Wednesday 2 December the self-isolation regulations changed in England - see here - these now exempt participants of ethically approved coronavirus research (like this study) from multiple periods of self-isolation if they have repeated positive swab tests within three months (90 days) of their initial positive test.
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We were worried that my daughter having tested positive would have to isolate for another 10 days when she was tested in subsequent months, but the above rules prevent that. In reality we just haven't had her tested the last two times, first one because I was unaware of the above, and the second time as she was out when the ONS people came round.