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.
HMRC are correct because there has been a disposal for CGT purposes. The cost of the shares disposed of is the sum of what you paid for them and the gain on which you paid income tax. That will probably equate to the market value of the shares on the day you exercised them so there should not be much of a gain, if there is one at all. The cost for CGT purposes of any shares you retained is calculated on the same basis. Write to HMRC and give them a calculation of the gain or loss.
I hope this helps but let me know if you have any further questions.
You have a capital loss of $303 which you can offset against gains you made in the same tax year. If there were none, you can carry it forward to use in future tax years. You will have no CGT to pay. If it were not done the way it is, you would end up paying income tax and CGT on the same gain, ie double taxation.
As you have paid the income tax due on the shares you retained, you will only pay CGT in future if you sell them for more than their CGT cost, the method of calculation for that being given in my previous post.