Hi Prunella,
I'm a mortgage/life assurance broker and it really just depends on your specific circumstances. Whereas I can't say exactly how the underwriting will go on your policy, it is vitally important that you disclose all the relevant information to the life company so that they can make an informed decision.
If your partner is in good health, it may not have a hugh impact on your policy. He will probably be asked to go for a medical examination with an independant GP. This isn't anything out of the ordinary so don't worry. If the company decided that they would consider him a "higher" risk, then they may put your premium up - how much they would put it up varies from one case to another.
If I were you, I'd apply for the policy BUT don't cancel your existing one just yet. At least then IF it turns out for the worst, you can just keep your existing policy in place.
In the event that the insurer refuses your partner OR you decide that the premium is too high etc etc your alternative option would be (assuming you still want to go for the mortgage) as Clubman suggested; the bank may allow you to waive the life cover(I'd advise you to avoid this though if at all possible).
A better option might be to keep your existing life policy & see if the bank may even agree for you to waive PART of the life cover requirement.
Hope this helps a little but if you need any further advice in relation to this OR your mortgage, don't hesitate to contact me.
Regards,
Caroline.