Hi,
I'm a GAD sufferer (generalised anxiety disorder) and it massively messed up my sleep. I averaged about 3 hours a night for 6 months and as a result my anxiety obviously got a lot worse!
Unfortunately (as you know) there's no magic pill and absolutely no sleeping tablet in the world that doesn't have side effects :( I discovered this over a number of months and I'm still convinced half the natural remedies are snake oil.
Anyway, I drifted from one thing to another for months until I bit the bullet and just decided to do the very boring thing and follow standard medical advice (move more so you're physically tired, have 30 mins before bed time with no screens etc etc). Here's my routine now and I now sleep between 7.5 and 9 hours a night with no problems:
I swim for 30 mins 3 times a week at 9pm, wash hair and dry it at the gym and go to bed as soon as I get home. Sleep like a baby.
If I'm not swimming that night or dont do anything active, I run a very very hot bath, then before i get in it I take a very cold shower for 3 minutes. I then go straight from the shower into the hot bath and somehow it simulates physical tiredness.If you don't have access to a bath you can do the same thing with just the shower.
I have dim lights in the bedroom and bathroom and stay in darkened rooms for 30 mins before bed (during bedtime routine). It's hard but you must must must avoid looking at your phone or any screen for 30 mins before bed. This is the 1 thing that made the biggest difference for me.
Finally, no drinks for 30 mins before bed. I take a pint of water to bed with me to have on the side in case I'm thirsty in the night, but otherwise don't do anything in those 30 mins before sleep other than brush teeth/ skincare etc etc.
Finally it sound daft, but make your bed properly when you get up and tuck the duvet under the mattress so it's slightly restrictive when you get in (a bit like hotel beds). Studies have shown you sleep better when "swaddled"/ with constant light pressure on your body. I do this now and it definitely makes you fall asleep faster :)