It is difficult to give a precise answer to this without a lot more information but I'll try and help with the general areas which need to be addressed.
Firstly you and your partner need to consider what exactly is being sold - do you own shares in a company that carries on a business, or do you both jointly hold some assets (eg machinery, pcs, cash, trade stock?) The other valuable asset is known by accountants and taxfolk as "goodwill" - this is basically the difference between the overall value of the business and the sum of the individual assets. This is the value which you have added by making the individual assets into a business.
Once you know what you are selling, then you can allocate the £40k amongst the assets on a reasonable basis. You will want to take into account the tax consequences of each category of asset.
There are 2 main tax reliefs which you may claim. The first is your annual allowance for capital gains of £7,700. The second (and possibly more valuable) is business asset taper relief, which exempts part of the gain according to how long you have owned the assets provided the assets meet certain requirements. In the most recent budget it was announced that only 25% of a gain would be taxable if the assets had been held for 2 or more years.
CGT only applies to the gains made, so you can deduct any costs in acquiring the assets (so for shares, deduct the cost of the shares, and for other assets the original cost). There will be some assets not chargeable to capital gains (eg most plant and machinery, cash and trading stock) ? goodwill is usually the most common asset to be taxed on the sale of a business. However there may be other tax aspects to be considered if you own the business directly (and not through a company).
However to give you a rough idea, lets assume that the whole £40k was attributed to goodwill in a business that you have owned for more than 2 years:
Gain of £40,000
Business asset relief of 75% (£30,000)
Annual Allowance (£7,700)
Gain subject to tax £2,300. This gain would be added to your total taxable income for the year, and effectively taxed at your highest rate, so probably 22 or 40%.
You should really get some professional advice , as you should be able to reduce any tax bill provided that you plan the transaction appropriately. Look for a local chartered tax adviser or chartered accountant with tax experience. It is important that any sales contract is correctly drafted for tax. For example, if the sales contract indicated that you were getting £40k in exchange for promising not to set up a rival business, then the £40k would be taxable, and you would probably not get business asset relief.
This is the IR guide to capital gains - www.inlandrevenue.gov.uk/pdfs/cgt1.htm. Section 7 covers business asset relief.