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One of my closest friends is a senior civil servant who transferred into the civil service from the military and occsionally works in Downing Street.
The issue of this supposed security threat is what winds him up most. To paraphrase him, "driving to your parents house for your mum and wife's birthdays is not on the list of sanctioned actions for staff who are close to the PM and feel under threat".
And the police will have a record of any credible threats. I imagine if they had these, it would've been released by now.