Renting with CCJ

Hello

I am relocating from Manchester to London for work purposes. I have a secure job and have managed to secure a transfer to another unit in London. My husband is a bus driver so he has just been offered a job with stage coach , whom he currently works for in Manchester .
We have excellent current landlord reference , employment references , savings and will pass the income test for rent.
The only thing holding us back is a CCJ - which I appreciate is a huge thing and will impact landlords insurance.
The CCJ is in relation to a personal loan that I took out for private medical treatment (operation)… and got into difficulty paying this back. Circumstances are different and I am paying this back now and have been for many months. The loan amount was £5k however due to interest increase to £8k.
We have a guarantor available for if we find a property that’ll rent to us .

How can I enter negotiations with landlords? I can truly appreciate their hesitation to rent their property to someone with poor credit history, after all it’ll be worth a considerable amount of money and quite rightly they want to protect and minimise risk .

We have never missed a rent payment ever…but that goes without saying so cannot use this as a positive…
we are looking for a long term let and have until end of august to find somewhere …
2 bed property within 10 mile radius of Wimbledon.

Any ideas to help negotiate with landlords?

Thanks