Hi hablitza tamnoides
If you move within your current Local Authority then you can do so without having to claim UC, you don't need to make a new claim for HB, your existing claim will be modified.
If you move to another Local Authority area before 27 January then your SD Premium bars you from claiming UC and you can make a new claim Housing Benefit and retain your ESA.
If you move on or after the 27th then you will need to check back as the "SDP Gateway" is due to be removed on this date and moving to a new LA will result in you having to claim UC, however, you should be able to get Transitional Protection of your SDP payment. At present I cannot tell you if the "SDP Gateway" will be removed due to everything that going on, but members will be notified in our news letter as soon as we know.
If you have to apply for UC then you will also need a 'fit note' to send to your work coach. When UC was built there were no electronic connections to any of the benefits that it replaces, such as ESA(IR), so if you have to make a claim for UC it knows nothing about any ESA award, hence the requirement for the Fit Note, your ESA claim will be manually, transferred to UC.
Gary
Nothing on this board constitutes legal advice - always consult a professional about specific problems