score:6
The simple answer is that nobody can tell you.
That's not to say that nobody knows, but anyone that does know would unable to share such information publicly.
The US and the UK do have extensive data sharing agreements, many of them as a part of the "Five Eyes" alliance. It is certainly very feasible (probably even likely) that such information would be shared under this agreement, especially as the basis of the travel ban you refer to is (at least in theory) related to terrorism.
You should also keep in mind that what you are suggesting would entail lying on your ESTA application, and fundamentally entering the US illegally under the Visa Waiver Program. If you are caught, you can expect to be deported, and barred from entering the US for at least several years (not necessarily officially "banned", but your odds of having a visa application approved after both having visited Iran AND having been caught lying about that fact, would be low).