Managed migration to UC .

Hi,
I have had a few days of major concern, 're my private pension payments, and after ......finally.... Getting through the DWP switchboard after 1 hour 40 mins, have received positive clarity from them about my situation. I receive contribution based ESA, topped up with income based ESA. I have been on ESA since 2013.
I also am in the support group,and have all the various severe disability components.
I started receiving a very small pension 6 years ago ( at age 56) and because the sum was far smaller than the contribution based ESA limit of £85 per week, ( I receive £130 per calender month), I never worried about it. I spoke to them today and told them my exact up to date calender month payments for 2025, and they confirmed that I did not owe anything, and had nothing to pay back.
My question is, I am aiming to do my migration at the end of April,(it has to be by mid may) how do I receive what I currently receive, when it's only my income based ESA and HB that are being moved across. If I was only receiving income based ESA, all my pension money would be taken as income, and I would be £130 per month worse off. Will I get this as part of a top up on migration, or will I get it via a separate payment from "new style ESA?
Many thanks , Chris.
I apologise if this is all very confusing,

Thank you David,
Yes I've done this again today, and they have contacted my local CAB to call me next week, because they want to be sure that I'm on both forms of ESA. I presumed I must be on both because when I explained with the DWP on the phone yesterday that I had been drawing on it since 2019 and hadn't thought to tell them, because my weekly amount was tiny compared with the contribution based ESA, they checked everything, and said that I owed them nothing at all, and nothing would change until my migration. I have taken details of the call, time , office region, name of contact, etc...
I was so pleased with the outcome, I didn't ask if they would be sending me an updated printed breakdown, with the change of the addition of the pension, but I'm sure they will. They have all the information, and I was very relaxed, until this morning when I tried to do my migration calculation with the CAB dedicated line. They have told me not to worry and the DWP call will be recorded etc.. I will wait for a call next week from local CAB, and hopefully, a letter from DWP.

After some searching this evening, I have found a letter from the DWP from June 24, stating that as I have a contributory element with my Esa... Blah blah... and included my tax entitlement limits etc... So ..... I do have in writing that I am entitled to both elements. Hooray for me not throwing anything out. Shame I've got such terrible memory though, the letter was less than a year ago.haha. So, back on the phone to CAB on Monday for a transfer calclation.

Personally I would recommend the CAB Helpline 0808-223 1133 and 0800-1448844. They're the most experienced advisers. Local CABx for their best, but the level of experience does vary.
(I speak as an ex-advisor 🤭).