Sounds very much like liver dump or dawn phenomenon: our liver dumps glucose into our blood to "help" us wake up and get on with the life of the day.
Sweetener has been known to raise BGs in some people too. It doesn't do that to me but I have other bad side effects so tend not to use them.
I have a couple of cups of tea with whole goat's milk every morning and I find that's enough to stop liver dump happening. Yep, we're all different and need to experiment with what's best for us personally.
Just normal teaI would add that the milk in the tea could be a contributing factor as well as the DP ( dawn phenomenon )
edit -- unless you mean "white" tea -- I think that is the quite expensive stuff popular in London tea rooms these days -- if so - forget my milk comment
Bg at 06:10 11.5 than just tested again at 08:15 and it's 15.9 (why)
As already mentioned, probably liver dump. I have read several suggestions as to how to switch it off, a small snack before bed or as soon as you wake up. It's something that you might like to Google, there's so many ideas to try. I do find that small snacks seem to help.
Did you sleep well? A bad night can also raise fbg levels.