This paper analyzes the principle of insulation gain in high voltage vacuum interrupter with series-connected asynchronous interlinking between main and auxiliary gaps, focusing on a newly integrated structure. A simulation prototype of the vacuum interrupter with asynchronous interlinking between the gaps was constructed. The study explored how variations in the gap opening distances at different incoming line ends affect the voltage distribution and conducted experiments on the breakdown characteristics of series-connected main and auxiliary gaps. The findings indicate that the voltage distribution on the high-voltage side is higher, and the proportion of the total voltage attributed to the main gap increases with its widening and decreases as the auxiliary gap widens. Voltage partitioning measures significantly mitigate the impact of stray capacitance, ensuring a 2:1 voltage distribution ratio between the main and auxiliary gaps. When the moving end of the vacuum interrupter is the incoming line end, the insulation of the integrated structure of the main and auxiliary gaps improves by 16.25% compared to a single chamber with a gap of 15 mm, and with voltage partitioning measures, the insulation gain of the prototype is approximately 1.17, indicating substantial insulation enhancement. The research provides valuable guidance for the development of high-voltage vacuum arc-extinguishing chambers, with the potential to realize units for voltage levels of 252kV and above.