The AIA's (check whether you can claim the super-deduction, rather than straightforward AIA's, as you may be able to claim 130% of the cost as a tax deduction rather than 100%) are deducted from the trading results of the business.
For example, if your DH had £35,000 of income and £10,000 of regular costs, before the van, he'd have a profit of £25,000.
If he then bought a van for £15,000 that was eligible for the superdeduction, you'd then deduct £19,500 from the £25,000, leaving £6,500 taxable.
If he'd made a loss before CAs originally of, say, £5,000, then with the CAs included it would be a loss of £24,500 (i.e. it adds together). If he had a profit of, say, £5,000, the £19,500 would take it to a loss of £14,500.
He'd then be able to carry those losses forward and offset them against profits in a later year (i.e. you don't lose them, and you don't have to pay any tax on the year the losses were made). It doesn't matter if you're on a cash or accrual basis, it can still be offset.
Please note - if the van is second hand you can't claim AIA's - you'd have to just claim regular Writing Down Allowances (WDAs).
Also, further point to note, if you do claim the superdeduction, as and when he sells the van further down the line, he'd have to account for 130% of the sales proceeds through his tax return to compensate. This is only an issue if you're likely to sell something for more than you bought it for, in which case you should just claim AIA's, rather than the SD, but in most cases assets depreciate, so you're not worse off, but it's just a little technical point that I suspect will get overlooked and HMRC will take great delight in finding.