Is there any way of avoiding Capital Gains Tax on my second property?
Peter is not correct. The 3 year exemption applies only when you have lived in the property. As it is now too late to make a PPR claim, the only way to mitigate your liability is to live in property A for a while and establish it as your main residence. You would then be eligible for the 3 year final exemption, as well as let property relief of up to £40k. Are you married? If so, you could transfer half to your wife tax free and then you would both have your annual exemption available to set against your share of the gain. The rate of CGT is 18%, not 40%.
