Hi,
If you are tax resident in Singapore and dispose of UK shares on a recognised stock exchange, resulting in a gain, then the gain should be declared in the UK on a self assessment tax return. Tax may be payable in the UK.
In Singapore, this would be a taxable income/gain.
To avoid double taxation, you would need to claim a tax credit for UK tax paid, so that you do not pay the tax twice. Article 13(a) of the UK Singapore tax treaty, covers capital gains tax and can be found at:
Singapore: tax treaties
Thank you.