Hello anthonyfromcroydon,
Welcome to Apple Support Communities. We'd recommend starting by isolating whether this happens on all accounts or seems to be related to a specific account.
If this happens with one email account or you do not have multiple email accounts on your iPhone and Mac, test in your provider's webmail to see what happens there. When you read an email there, does it sync? If so, which device syncs this change?
Next, use Mail - Official Apple Support to find your email settings by entering your email address. You can then make sure those settings are correct on your devices. From iPhone, go to Settings > Mail > Accounts > [Account name] > [Account] > Advanced. From Mac, go to Mail > Settings > Accounts tab > Server settings.
Best of luck.