Why would they be taxed again? You haven't paid tax on the assets once, let alone a second time.
Let me give you an example:
I buy a piece of equipment for my business for £10,000. I claim capital allowances on it over several years totalling £6,000. That leaves unrelieved expenditure of £4,000. If I dispose of the asset either to a third party or my company for £3,000, my net cost is £7,000 (£10,000 - £3,000). As I have already had capital allowances of £6,000, I am entitled to a balancing allowance (a deduction from my trading profit) of £1,000 (£10,000 - £3,000 - £6,000). You never get more allowances than the net cost of an asset.
The buyer of the asset introduces that asset into their business at a cost £3,000 and they can claim capital allowances up to £3,000.
If I had sold the asset for £5,000, my net cost is £5,000 (£10,000 - £5,000). I've had allowances of £6,000 so there is a balancing charge (an addition to my trading profit) of £1,000 (£6,000 - £5,000).
If you sell a fixed asset for more than it cost to buy then you may have Capital Gains Tax to pay if your total gains in a tax year exceed £10,900.