No it wouldn't, booster pumps need to be able to sense the pressure of the water in the pipe work and this pump wouldn't do that. This is what I use https://www.machinemart.co.uk/shop/product/details/cbm240e-1in-multi-stage-230v-booster-pum
I think quite a few use this as a booster pump.
mine doesn't sense the pressure and works fine , the switch on the clarke one is a flow switch that shuts off the pump if/when the flow stops , if you are there to do this yourself you don't need it .
It would still be no good though as its only 13m head .......you need around 48 metres head (around 85-90 psi).