I am employed full time and wish to do some freelance work as well, and as I understand it I will need to register to be self employed and fill in a tax return.
Yet, would I have to inform my current full time employer? Would there be any tax implication that would affect them?
There is no need to inform your current employer from a tax perspective - it doesn't affect how they calculate PAYE tax and National Insurance on your salary.
When you submit your tax return after the end of the tax year you will include the figures for your employment income alongside your earnings from self-employment so HMRC can calculate the correct tax due on the combined figures.
Slightly off-topic but you should check what, if anything, your employment contract says about doing other work. Some employment contracts forbid outside work, or require you to inform your employer. There is more likely to be an issue if there is an actual or potential conflict of interest between your employed and freelance roles.
