Hi,
When you purchase a second home you must write to HMRC, to advise that your first property will be your main residence, for Private Residence Relief purposes. You can see guidance here:
Tax when you sell your home
If the Private Residence Relief is 100% of the gain arising from the disposal of your main residence, no Capital Gains Tax is payable and no gain is reported.
You will need to advise HMRC of the change to your main residence and update your personal tax account, to reflect your new address
Personal tax account: sign in or set up
Guidance on stamp duty can be found here:
Stamp Duty Land Tax
Thank you.