Mortgage impossible?

Hello,

I am looking for advice on my current situation.

I live with my partner in a rented house currently paying £650 in rent. My partner has a mortgage on a property with equity of around 18k possibly a touch more. This property is currently rented out covering costs.

We both have an income each, 26k for myself and 27k for my partner. The problem lies in our credit card debts. My partner has debts of 25k and me of 6k. We recognise that this is a problem. We are paying them off but very slowly.

We can't go back to my partners property as location of job will not allow, hence the rented property.

We realise we have made mistakes in terms of financial decisions in the past.

Would a new mortgage be impossible? We would be looking at a new property of around 120k. The frustration is that our incomes are good but our debts probably make it difficult or impossible to borrow.

One possible solution I thought of could be that we try and save for a deposit and probably get help and get a mortgage in my name?

Many thanks in advance.