This is probably a once in a lifetime opportunity, do not waste it.
If inflation is 8% then in one years time that £80k is worth £73,600.
If that stays then in two years time it will be worth £67,712.
What you want is for the £80k to grow and not be “penalised” for it.
What is the interest rate on your debts?
If it is less than 6% then keep the debts.
If it is more than 6% then keep the house, move into it, get a mortgage for £20k and pay off the debts. Your mortgage might be about £140 a month, depends how long you want the term. Most people would jump at the chance of buying an £80k house for £140 a month.
That house might be worth £88k in two or three years time.
When you retire it will be worth more than £200k.
This could be a leg up you leave for your children when you pass.
There may be one more option for you, and that is to get as much of it put into your pension as possible. You could sell the house, pay off the debts, and increase your pension contributions to 80% of your earnings (£19,200), the government would then add £4,800 tax relief so you have £24k in your pension. Whilst putting all your wages into your pension use some of the house sale proceeds to live on.
So for the first year you pay off £20k debt, put approx £20k wages into your work pension, and use £20k house proceeds to live off (in place of the wages).
Of course you will lose benefits however much that is so you will need to factor that in, let’s assume you get £10,000 a year in benefits. So you need to use a further £10k of the house proceeds to live on.
After 1 year you will have £40k left, so you again put 80% of your wages into your pension and live off the house proceeds. So after 2 years you have £10k left. You could have used this in the 2 years for a few luxuries / holidays / house improvements or just put it into your pension in the 3rd year.
You can then claim Universal Credit again but have £48k in your pension but have “lost” £20k of benefits but gained £8k in pension Tax Relief so only £12k “down”.
£48k in a pension with an average stock market return will double every 10 years, so also be over £200k when you retire.
You could maybe even do hybrid by putting it all into a pension in one year but lose the tax relief on non-employment contributions. So you stop your UC claim and payoff the debts. You work and put £19,200 earnings into your pension and it gets topped up to £24k. You can also open a private pension (SIPP) and put in the remaining £40k. So you have no debts and £64k in your pension. Then after some months you claim UC again. I don’t know how many months you would have to wait though to side-step the deprivation of capital issue.
Pensions historically have grown more than housing, but you can’t live in a pension and you will lose the benefits this route so on balance I think keeping the house and getting a small mortgage on it would be the sensible thing to do. The pension would be the best thing to do if you were not on benefits.
One last point… if you are earning £24k you will take home about £1.7k a month, and if you do get £10k benefits then you have a further £830 a month, so over £2.5k a month, which is the equivalent of a £38k a year job. In which case you are not poor.