I have renewed car and house insurance as a new quote for more than 10 years.
The new quotes have always been cheaper.
Even though the question regarding who the previous insurer was, is stated as the existing insurer, the new customer discount is usually still applied on the new quote.
In many cases, I renewed the insurance through onebigswitch and received an extra discount.
Car insurance quotes are usually cheaper if a spouse is included for cover, compared to a quote for one partner only.
I always experiment with adding larger car valuations and yearly mileage. If the online quote is not increased as a result of this, I include the larger figures.
If you include lower figures, you run the risk of being quoted for an extra premium of you need to increase these mid term.
If your quote is at the minimum premium level, try adding extra cover to see if the quote increases. If it does not increase include the extras. For car insuranc, extra no claims bonus protection could be included, or lower excess amount.