As the problem only happens with Microsoft email accounts it may well be that Microsoft are the problem however as you are involving three email services, BT, Microsoft and Gmail to get your email the problem could lie with any one of them and may not be easy to track down and fix the problem.
There are similar posts on various other forums which suggest the problem is with Microsoft emails not complying with gmail's anti spam requirements.
I am assuming that gmail is your preferred email service because you are forwarding everything to it.
Why don't you instead of forwarding all the email that arrive in your BT email account to gmail have gmail set to access your BTMail account so that you can deal with the emails from within gmail.
This is easily done in the gmail account settings. It will in effect make gmail behave in a similar way to an email client and cut out the need for any forwarding.
The alternative is to set up an email client such as Thunderbird to access both your BTMail account and your gmail account and use that in order to manage your email.
