When using our UK website hosting or UK email hosting this usually happens because the nameservers on the affected domain have been changed to make the domain work with Farbyte's servers, but the domain itself has not been transferred in.
There is a brief period when some remote mail servers direct mail according to the new MX records, but the local mail server is still seeing the old MX records.
This causes the mail server to reject mail until the old records expire.
That usually happens within 24 hours.
Domains which are fully transferred by-pass the MX record lookup and so are not affected by this problem.