Thank you for the question. I would advise providing them with an agreement signed by both yourself, and your partner stating that you authorise the landlord to move the tenancy into your sole name. If you provide them with this then they should be satisfied they have authority to move the tenancy. However, what they are worried about is the if this is moved to your name, and your ex partner does not reside there and has no place to go, they will not be allowed to get a house based on homelessness as they will have, as they said, intentionally made themselves homeless and will not qualify, therefore this is something you will have to consider prior to moving the lease over to your name. You don't specifically need a lawyer to draft up this agreement, so long as it is clear and contains the information the landlord needs.
I shall provide you with a helpful link that will assist you in finding a solicitor/representative near your local area. This will provide you with someone nearby your area who can assist you if required.
I hope this information proved helpful. You will find a local solicitor who deals with these matters on the law society webpage which is as follows;
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