For anyone still waiting from November, here's what I'm doing in case it's any help.
My approval date was 18 November 2020.
I first wrote to my local council, who said no certificate has been received for me. If you're lucky, they might have received a certificate and they might be one of the councils that doesn't care about the Home Office invitation letter (Wandsworth isn't one of these councils).
Then I wrote to
citizenship.support@homeoffice.gov.uk (the contact address in the approval letter PDF) and
CT2caseworkenquiries@homeoffice.gov.uk (the contact address in the e-mail to which the PDF was attached; presumably you might have a different address in your e-mail as 'CT2' might be a specific team assigned to my application route). The e-mails ask them what the hold up is, referencing other applicants posting on immigration forums who are receiving invitations based on substantially later approval dates.
That was a week ago. I expect I might get a response around the end of May. Since it is probably going to take so long, I have also submitted a complaint using the form here:
https://www.gov.uk/complain-uk-visas-immigration. There were no appropriate options in this form, so I chose what seemed to be the nearest appropriate complaint reasons: 'Waiting for a decision or documents' -> 'A decision on an application'.
I used the Home Office Ref # from the approval letter in the form. The text of my complaint was basically:
"I am complaining about the length of time UKVI is taking to print and mail my citizenship certificate and ceremony invitation letter following approval of my naturalisation application on [date]. You can resolve this complaint by sending out the necessary documents for me and my local council (Wandsworth) to complete the citizenship process."
Note that UKVI has a separate complaint form from the general Home Office one, so don't get caught out and have to wait another several months.
I haven't yet tried my MP. I will try them if I don't hear anything (or hear something useless) within 20 working days (morning of 30 March).
Hopefully this will all be unnecessary and I'll receive the letter soon. But if I'm subject to the dreaded 'technical error', the sooner I complain and start the months-long process of getting someone to respond, the better. If you're still waiting based on a mid-November or earlier approval, you might also want to start the process.
I live one mile away from the city centre and still have to wait 10 days.
congratulations. Have you applied for passport?
Timelines below:
