I have three solutions for anyone to try as I had similar issues especially with push notifications from my ring door bell whe on mobile data.
1] A silly thing but my APN settings were all correct except the naming which I had as Virgin Media. Change this to Virgin Mobile and save the setting. I don't know if this was the answer as I did number 2 below at the same time. However my notifications are now instant whether VPN is on or not.
2] Use a VPN (no need to pay) try Hotspot Shield free, to start with. You Get 15 GB throughput a month for free so might be enough for some. Just keep closing the offer to try the premium version at first, to try the free version VPN. If it works for you, as it did for me, I'm thinking of going premium.
3] If you have a dual sim phone like i have and have both sims activated change the preferred network for SMS to the other sim in my case a 3 payg. The only problem with this is my credit on my payg is down every time someone rings my bell. Therefore use this if the above doesn't work for you.