You will be truly British once you register on feddit.uk
In seriousness, I like to think it's a state of mind. If you find yourself generally aligning most with the more positive British attitudes, you're British. Though living in Wales, you may end up feeling more Welsh eventually!
If you want to feel more connected, try getting involved with local festivities and traditions.
Explore the countryside with the Ramblers. Do some pub quizzes. Go to a folk festival.
The sorts of things that involve you with pleasant people.