I have dual UK/US citizenship. I reside in the US and pay US taxes. I pay taxes on rental income and a small amount of business tax in the UK from once a year art show. I want to transfer the money in my UK account (made from selling real estate in the UK) to the US. I was not liable for capital gains taxes in the UK on the real estate because I am a non-resident. What are the US and UK tax liabilities for transferring 100k in Pounds to the US.

On your return a U.S. citizen or resident must report your world wide income. If you paid taxes in the foreign country, you will claim credit for taxes paid in the foreign country by filing Form 1116.
Another filing requirement is Form TD F 90-22.1.
So you will report real estate sale on schedule D (Form 1040). Report rental income on schedule E (Form 1040). If you are transferring your own money, you do not pay any tax on the transfer.
Your U.S. Tax Return: U.S. Citizen or Resident with Foreign Income