Email Send/Receive causes slow access to website host server. Any Suggestions?

Question

Hello Community.
"Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth."
I have a bit of a weird problem and though it sounds silly, I'm 99% certain of the cause. My business migrated our five different sites to a new web host (shared hosting) about 5 months ago. Since then we've been plagued by a localised speed issue with connecting to that host. The host is a reasonably good one, but for some reason when connecting on our local network ONLY we were having intermittent load problems; anywhere for instant load to 40-50 seconds. After much testing we have arrived at an improbable conclusion; That accessing webmail (e.g. clicking Send/Receive) on any Mac within our network causes a massive and immediate slow-down of website access and smtp connection to any of our five sites held on the shared hosting server.
Again, I know how strange that sounds, but we've essentially proved it based on ping tests and side by side comparisons of isolated computers. The ONLY computers that are affected are the Macs on the network and also mobile browsers on multiple platforms. Windows based PCs are not affected by the slow down.
Also, the problem seems to be access based. By that I mean, one a site is accessed it loads almost instantly, but it can take up to 40 seconds of white screen before the site is reached. Interestingly, during this time, the sites' ping speeds are perfectly normal UNTIL the moment when the page is finally accessed and it loads instantly. Once the load triggers the ping speeds increase dramatically to the point where they occasionally time out. Once the site is loaded the ping speeds return to normal (approx 22 ms).
... help!
Important: Things we've ruled out:
ISP is not a factor (used a 3G modem to rule this out)
Router is not a factor (see above)
Switch is not a factor (Tested different switch)
Individual terminals are not a factor (when removed from the network or isolated on the network the individual terminals perform perfectly. Furthermore when an external mac (iMac laptop) was introduced to the network it performed just as poorly)
Browser/Operating System/CMS platform not a factor (multiple CMSs have been tested, testing on multiple computers with different versions of OS have been tested, and all sites have different CMSs; Joomla, Concrete 5, Bespoke, and Wordpress of different versions)
Cpanel setup not a factor (Each site has its own Cpanel account, the are not set up as add-on domains. Furthermore, a similar slow down has been observed on other sites held on that server)
Mixed platform network not a factor (We removed non-mac based computers from the network and turned off wi-fi to isolate and found no change)
DNS does not appear to be a factor (We tested multiple DNS including Googles 8,8,8,8 / 8,8,4,4 and found no change)
Cabling does not appear to be a factor (though the cabling isn't perfect, it's at least Cat5/Cat6, plus it wouldn't affect only our sites)
Email Client does not appear to be a factor (accessing email via Outlook or Mail App causes the slowdown)
Important: Things that we suspect
Computer Year of Manufacture: (though all computers are affected, the problem is most severe on pre-2013 constructed models (regardless of OS)
POP3/SMTP request immediately triggers the slow down (observed visually as well as in ping tests. No mail needs to be sent/received during this process to trigger the slow down, simply the request causes the spike. We haven't yet been able to test IMAP)
The Networked Macs (not the individual macs): (the individual computers when isolated on the existing hardware perform fine. Only when they are networked does the slow down occur)
DNS (Even though we've found no link to DNS, if feeeeels like a DNS issue.)
CHANGE of host. (We changed hosts due to extremely poor service and tech support. The new guys are fantastic. Though I don't think it's the new host's fault, it's possible that the change of hosts has caused our network to search for our websites in the wrong place)
Apple Knows Best: Is there something that Macs do with Mail to update a routing table? Like, could a mail application trigger an update to a local routing table?
Has anybody heard of anything like this before? Or can anybody suggest any possible things to test or change? Even though email requests seem improbable, I can confirm that it has been proved visually and through tests. As you can probably tell, our testing has been extensive so if you notice anything in our test  conclusions that I could add to please... I'm seriously open to suggestions now.
Any help with this would be much appreciated.
Kind Regards,
-TheWebFella

Answer 1

Hi Linc
Thanks for the suggestion. Yeah I'd already tried that. It's been deactivated on most of our computers already. Plus like I said, it's different browsers on multiple macs and also some mobile browsers on both iPhone and Samsung on our wireless network. I can confirm that on mac the problem is consistent across Chrome, Firefox as well as Safari.
Thanks anyway! Any other takers?