I decided to do a quick check on the two domains. Both have SPF records
albionmobility.co.uk. 3600 IN TXT "v=spf1 include:spf.protection.outlook.com -all"
chartwellinsurance.co.uk. 300 IN TXT "v=spf1 include:spf.messagelabs.com ~all"
Although neither of them appear to have DMARC records.
If Greylisting and the sending server are behaving normally then mail shouldn't just vanish. (I add both prerequisites because I recently came across a case where a server didn't follow normal SMTP guidelines).
Greylisting is an attempt to defeat fire and forget spam. Normal SMTP delivery stipulates that in the event of:
The receiving server not responding.
The receiving server sending back a 4xx error code.
That the sending party tries again. (It's important to note that a majority of clients such as Outlook don't do this but a mail server always should.
In the event of a timeout limit being reached (which can be from several hours to several days) The sending server will eventually report a delivery failed message, but in the majority of cases mail should be delivered within about 15 minutes of the first attempt.
Spam senders often try once and then give up and move on rather than attempting to redeliver to the same server. Which is why greylisting can help reduce spam. BUT it's not foolproof.
I do agree with @Lisa_CC here. Trying to find out what's happening with an email usually starts from the sending side. The companies involved should be able to see logs of the email transactions, including whether or not the mail send was accepted.
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