Hi. My name is*****'m looking at your question now and will post my answer or ask for more information here in a short while.
No CGT is paid on assets held at death.
Your estate assets will be valued for probate and whoever inherits the flat will have a base cost for it for CGT purposes equal to its value when you die. Your estate will be liable for Inheritance Tax at 40% on the excess over £325,000. If you are widowed, your executors may be able to claim the unused part of your late spouse's nil-rate band. You can read about that here and here. Potentially, you could have a nil-rate IHT band of £650,000.
I hope this helps but let me know if you have any further questions.