Online progress completed after 4 months, no correspondence or no action taken re. tax refund

I believe I have a very simple case of overpaying tax in a previous year through PAYE, and am due a refund. I raised this details at the start of May under 'Update income details' on tax.service.gov.uk from my online personal tax account - after 4 months the the status under 'check progress' has finally been changed from 'received' to 'completed'. However no changes to my tax code have been made, and I have received no email, letter or message in my HMRC with any information about this. I would assume this means HMRC disagree about me overpaying tax (It is quite cut and dry to me that I did, and by a decent amount) but is it correct to not get any information when the progress is updated to completed? I would have expected to at least get some response about why this is or isn't the case? Or is it simply that I don't hear back and have no means to discuss this.. Thank you

Hi,
 

A letter would usually be issued when this has been reviewed. If you have not received a letter within three weeks of when it has updated to completed you will need to contact our Income Tax department : Income Tax: general enquiries  . Thank you.