Hello, the land registry document you provided shows Hugo West under the charges register as a beneficiary. This is not necessarily your landlord nor will have anything to do with the agreement unless it is specifically stated that Hugo West is your landlord on the agreement. The land registry document will only tell you who is the owner of the property, whether by freehold/leasehold and this is the only information that is relevant to you. For clarity - the land registry document has no bearing on any contractual lodger agreement you have, except to tell you who owns the property.
To be a lodger, it is clear, the landlord himself must be living in the same property as you and sharing common facilities.
If you have a lodger agreement, you will know the agreement will be for a fixed amount of time e.g. 12 months from January - February. If there is an agreement that says one month notice, then you must give that one month notice. If there is no specific notice, then you must give notice in line with how frequently you pay rent e.g. if you pay weekly, you give 1 week notice or if you pay monthly then give 1 month notice. It just has to be reasonable.
A verbal notice, or sms or in writing are all ok if you are a lodger. You do not need a written notice to leave, though one is preferable.
It seems you have the address for service with an agent signing on behalf of the landlord, so if you wish to sue for your deposit back then you should use this address.
From my understanding your notice is one month as per your agreement so as long as you are not in a fixed term, then you can give your notice and leave, if you wish.
I hope this helps.