I had the same problem on my Series 3. I tried using a one way valve at the rear of the car but it made no difference. I went down the electric pump route using one of these:
https://www.ebay.co.uk/itm/371974766532?mkcid=16&mkevt=1&mkrid=711-127632-2357-0&ssspo=OUd2zYVDSHq&sssrc=4429486&ssuid=-6dTF2wzQl2&var=&widget_ver=artemis&media=COPY
I also fitted an inertia switch into the supply feed of the pump so that the pump will stop in an accident.
I now turn on the ignition, wait a few second and the engine starts on the first crank.
Nigel.