After emailed to different workshops who are able to do wood cutting in London, there is a studio called Lasercutworks accepted my request. Laser cut would be the quickest way for large-scale wood cutting. I also asked London Art Workshop, the guy also suggested me to do cutting via CNC Rounding due to that I need to joggle.
I went to lasercutworks for enquiring how to do timber cutting and the problem of joggle method. What they said is to do dove tail between each small piece, and cut an angle to fit in or use hexagon wood board to hold the top part of the dome. Please see the pic below:
The specilist is very nice there and helpful. And there is a student discount for students for lasercut! 50P / min which is the same in uni I think.
Here is the processing of lasercut:
And here is the phot with them! (Jared).