As Clubman said, each year the base price before discounts will rise however if you decide to chop and change to avail of discounts, heres what involved;
1) You will need to fill in new proposal forms.
2) The insurance company you apply to for a new policy will need to underwrite you, if you are ordinary rates then a new policy can be set up quickly. If further medical evidence is required then you are dependent on how quickly doctors can facilitate you.
3) Once the new policy is in force, you will need to assign it to your mortgage provider.
4) You will then need to get them to release the assignment of the old policy so you can cancel it.
There is some work involved but its not too bad especially if you are facing a large premium and the discount is significant, then it can be worth the effort. Do bear in mind though that you will face a larger premium in all likelyhood the following year though as Clubman mentioned.