I’m a first time buyer and am about to pay deposit for my new home on Friday. What i don’t fully understand is when should I arrange for the home insurance on the new property to begin from? Should the cover have started on the day I pay the deposit or after?

You need to insure the building from the date of completion, as the property is legally yours from then on. If you aren’t moving in immediately there will be a few exclusions that apply due to it being an empty property, but it is still vitally important that it is insured from that day onwards. You don’t need to add the contents insurance until you actually start to move stuff in.
Don’t forget to check that your insurance policy covers goods in transit from your current policy to your new property.
Ask your mortgage lender for a quote then compare it to quotes from other insurers – it may be a lot cheaper to insure through someone else.
Best of luck in your new home.