Hi
From the limited information supplied, I have assumed that these royalties are due from your late father creating literary, dramatic, musical or artistic works.
Since you’re not the original creator of such works then the selling of the rights to the royalties of such works will be subject to capital gains tax.
Intellectual Property Rights: copyright
At the time that your father passed away these works would have a market value.
If you sell the royalties for more than their market value then then capital gains tax would be chargeable.
To work out how much you would pay see :
Capital Gains Tax: what you pay it on, rates and allowances
In the meantime, any royalty income received will be chargeable under the miscellaneous income provisions and needs to be reported to us.
Authors and literary profits: royalties to person other than author