Depends on your timeframe and when you are drawing down the loan. In my experience it takes a month to five weeks to get these policies issued and assigned ( maybe longer if there are medical issues) to the lender so if your first application is at an advanced stage and you need the dosh quickly you might be as well leaving it go ahead. You can then proceed with la brokers to get cheaper life cover and then assign that policy to the lender who will then reassign the other policy back to you and you can cancel it. This advice might be even more pertinent if a postal strike goes ahead.