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In general, any gain made on a property is chargeable to capital agains tax. There are reliefs and allowances available to mitigate the chargeable gain and therefore CGT.
If you have been renting a residential property that has been your main residence at some point during the period of ownership, then you are able to claim letting relief against the gain and reduce your chargable gain.
If the property is in joint names, then both of you would be able to claim letting relief in your own right. There is every likelihood you may not pay capital gains tax when you sell your property to buy another one of similar value.
In order to arrive at chargeable gain one would look at
total period of ownership
period covered by private residence relief as main residence
additional relief for last 18 months of ownership
further letting relief to a maximum of £40,000 per owner
and finally gains annual allowance of £11,100 per owner (current tax year allowance)
Once you have gone through the calculation you may find that what is left over is covered by gains allowance and no CGT payable.
More information on private residence relief can be found on hs283 here
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