The problem is your partner is named on your policy so is associated with you (in contractual terms) and the insurer sees you/your partner as more of a risk, hence the increased premium. The same thing happened to myself - the insurer bases the premium on risk so if you have points or been involved in any accident, fault or non-fault, they see you as a greater risk and charge you more.
However, you are covered under the Consumer Rights Act 2015 here which means you have a right to expect a service (from the insurer) carried out with reasonable care and skill. Furthermore, the policy should be “fit for purpose” and “as described”. If it isn’t then you can allege breach of your consumer rights and breach of contract.
You should now make a formal complaint and if that does not resolve the matter ask them for a "deadlock letter", which is a letter giving their final response. You can make the complaint here: https://www.rac.co.uk/complaints
Once you have the deadlock letter the next step would be to escalate this to the Ombudsman - they will investigate and liaise with the insurer which would hopefully result in a reduction of the renewal premium. They can order the insurer to make a financial award for inconvenience if they have acted poorly.
Once you have their final response, you can make the complaint to the Ombudsman here : www.financial-ombudsman.org.uk/consumers/how-to-complain
Or by email:***@******.***
Based on the circumstances, assuming the insurer does not uphold your complaint, I am sure the Ombudsman will do. The Ombudsman will look at this case independently and will make a decision based on what happened. Their decision is binding on the insurer.