There's a nice guide to what the self employed can do with losses here: https://www.litrg.org.uk/tax-guides/self-employment/working-out-profits-losses-and-capital-allowance/what-if-i-make-loss
The key list (there's more detail on each option on that page) seems to be:
You can use the loss in the current tax year and set it against all
of your other income including income from savings. This reduces the
tax that would otherwise be payable on your other income. This is
also known as sideways loss relief.
You can carry the loss back to the previous tax year and set it against all of your income including income from savings. This
reduces the tax due on this income, and a repayment of tax is
For a new business, if the loss occurs in any of the first four years of trading you can set it against your total income of the
three tax years immediately before the loss year, starting with the
income of the earliest year first. This reduces the tax due on this
income, and a repayment of tax is usually generated.
You can carry forward a loss and set it against profits of the same trade in a future year. This is generally the default position
if the loss cannot be used in any other way. This is likely to
reduce the tax that would otherwise be due in a future tax year.
If your business finishes and you make a loss in your last year, you can set this against your trading profits of the previous three
years, latest year first. This reduces the tax due on this income,
and a repayment of tax is usually generated.
I note none of the options is to carry losses across to another business. However the first option listed above of setting it against other income would appear to achieve much the same result if the other business is profitable. (I also note that HMRC's SelfAssessment notes on the Self Employment pages say things like "Carry your unused losses forward to set against any future profits from the same business")