Can my partner and myself have different levels of cover on a joint policy?

Yes you can - but we recommend you look into buying separate policies.
You can have different levels of cover on Joint Life policies (i.e. each person has their own sum insured), and if this is what you want, let the Life Insurance Adviser know when they call to go through your requirements and provide you with a selection of quotations.

However we may have a better option:
If you are considering getting a Joint critical illness insurance policy then we suggest you also cost up the option of separate policies for each person. This is because with a Joint policy, if one of you makes a claim then the policy the ends completely for both of you. This means that the other partner who did not make a claim has no insurance protection of their own, and it is likely to be later in life when it's either too late or very expensive to get a new critical illness policy.