Unfortunately there is nothing you can do to convince a lender to do something they don't want to do.
What you can do is ensure they aren't making a mistake in their approach, as it is not uncommon for a lender to say no, after misinterpreting their own criteria. So check through their criterea yourself or get a professional mortgage adviser to do it.
As an alternative to getting a personal loan, you could consider moving the entire mortgage to a more understanding lender who has a more relaxed approach to lending. A maximum LTV of 55% is rather low, so you will definitely have options available, depending on income etc.
Have a chat with an independent
mortgage broker who will be able to show the best alternatives to staying with your current lender, allowing you to make an informed decision on the best way forward.