Yes, it is usually possible to change mortgage insurance provider at any time. Over time different insurers can come out more competitive than others so it makes sense to consider changing insurer from time to time.
Drewberry reviews the cover and premiums for our clients every year to ensure they are still the most competitively priced given the clients requirements and suggest a change of provider if worthwhile.
It is usually necessary to provide an existing provider with 30 days notice before cancelling your cover and direct debit. It is also important not to cancel existing cover before new insurance is in place. If your health has changed at all since taking out cover you should speak to an adviser.
For more information please see the guide: Switching Mortgage Insurance provider
As for banks, switching clients’ Mortgage Insurance away from that provided by banks is very common as the monthly premiums charged by banks is sometimes as much as double than a whole of market search would offer.
In the past banks sometimes used to bundle the insurance premiums into the mortgage cost, so only a single premium is paid each month.
It is important to note that there is sometimes a penalty to separate out the insurance from the mortgage but it is usually the case that separation (plus penalty) is still cheaper.
If this applies to you then it is worth speaking to your bank to find out if a penalty would apply and, if so, how much the penalty would be so you can compare the benefits of switching to more competitively priced cover.