Meghan will not be a Princess and certainly not a Princess of the United Kingdom. The only Princess title she would receive is Princess Henry of Wales if he would not receive a title.
I think you are a bit confused about what is meant by the term 'of the UK'.
ALL the princes and princesses are 'of the UK'. They often use territorial designations but that is to distinguish which branch of the family they belong to and doesn't remove them from being 'of the UK.'
As a result as the wife of a 'Prince of the UK' Meghan will be a 'Princess of the UK'. She will be HRH Princess Henry of Wales and when Charles becomes King she will be HRH The Princess Henry.
What she won't be is HRH Princess Meghan.
She will be known as either HRH Princess Henry of Wales and then HRH The Princess Henry when Charles becomes King or Duchess of xxxx but she will still be a princess.
Remember that in the UK Princess is a lower style than Duchess anyway. The only wife of a Prince of the UK who uses the title of Princess is Princess Michael of Kent and that is because Michael has nothing better for her to use.
When Birgitte married Richard she was known officially as Princess Richard of Gloucester but when he inherited the Dukedom they were both promoted from Prince and Princess to Duke and Duchess.
Meghan will therefore be - HRH Princess Henry of Wales if Harry isn't promoted to a peer of the realm on or before his wedding day.
The 'of Wale', 'of Cambridge', 'of York', 'of Gloucester' and 'of Kent' are there so people can know which prince or princess you are talking about if there are two of them e.g. there are two Prince Edwards - one is 'of Wessex' and one is 'of Kent' but both of 'of the UK'.