ESA Support Group & SDP - Moving to UC area, HELP!

Since my husband died last year I have been living alone - he was my carer and I am moving next month to be near my sister as I am struggling on my own, but my biggest headache is what do I need to do re. benefits?
My income is: income-related ESA Support Group, and I am on higher rate of DLA for both care and mobility so I think my ESA includes the Severe Disability Premium.
I also get Housing Benefit & council tax benefit.
I am moving to a Universal Credit 'full service area' (Bath & North East Somerset)
A few months ago the government said that people in my position would no longer have to move onto Universal Credit, which previously had meant a reduction in benefits as there is no disability premium in Universal Credit - I had already worked out that I would lose at least £170 per month by moving, whereas if I stayed put until ongoing claims are moved from 'legacy benefits' such as ESA ('managed migration') there would be 'transitional protection' meaning that my income would not be reduced in the change to UC - until then, transitional protection did not apply to people making a new claim due to moving house.
Esther McVey made a written statement in June, Universal Credit:Written statement - HCWS745 which included the following:
'In order to support the transition for those individuals who live alone with substantial care needs and receive the Severe Disability Premium, we are changing the system so that these claimants will not be moved to Universal Credit until they qualify for transitional protection. In addition, we will provide both an on-going payment to claimants who have already lost this Premium as a consequence of moving to Universal Credit and an additional payment to cover the period since they moved.' (my italics & bolding)
www.parliament.uk/business/publications/...s/2018-06-07/HCWS745
www.disabilityrightsuk.org/news/2018/jun...e-disability-premium
So it looks as if I should be able to stay on ESA until 'managed migration' when everyone is moved over to UC and transitional protection would then apply.
BUT - I dont know whether this has actually gone through parliament yet - it was due to do so 'in the autumn' but I cant find out whether it has yet & what I need to do when I move.
Can I stay on ESA and just inform the DWP of my change of address?
And if I can stay on ESA, what happens about Housing Benefit? Do I apply to the local council as under the previous system?
I am hoping that someone in my situation has moved recently and might know what I need to do!
Thanks for reading, and if you can help I will be hugely grateful.

I contacted the CAB in my new area - a person who works for CAB & Macmillan and who already knows me as she helped me to sort out benefits out during and after my husbands illness.
She had specialist UC updates a couple of days after I posted this question and was told that
'Jan 16th is the key date - from that date going forward those in receipt of the SDP will not be able to claim UC so provided you move after that date you will stay on legacy benefits and keep your SDP'
and that if I move after that date I would claim Housing Benefit & Council Tax benefit from the local council.
I am a bit confused that you have different information - I hope my CAB advisor is right as it would be so much easier for me! My move is planned for late January (after the 16th).

If you think she is wrong please let me know. This whole situation is making a very difficult situation even more stressful.

Do you know when this will happen?
After the CAB advice I was confidently thinking that my moving date means I will just have to inform the DWP when I move, my ESA would continue without me having to reapply and I would have to contact the council for HB & council tax claim forms.
If this is not the case I would rather know in advance - and I would rather alter my moving date to a bit later if it meant avoiding the hassle of a UC claim etc. I am already struggling physically with quite considerable increase in pain levels from the pathetic amount of packing I've done so far, and I am fairly sure I will need a couple of weeks of resting after the move, including not having to spend hours on the computer which increases my back pain.