Traveling to UK with acquitted criminal charges

The controlling technical reference for this question is Part 9 of the Immigration Rules, entitled Immigration Rules part 9: grounds for refusal, and specifically Paragraph 320 sub paragraph 2, which states (in part)...

(2) the fact that the person seeking entry to the United Kingdom:

• (a) is currently the subject of a deportation order; or
• (b) has been convicted of an offence for which they have been sentenced to a period of imprisonment of at least 4 years; or
• (c) has been convicted of an offence for which they have been sentenced to a period of imprisonment of at least 12 months but less
  than 4 years, unless a period of 10 years has passed since the end of the sentence; or
• (d) has been convicted of an offence for which they have been sentenced to a period of imprisonment of less than 12 months, unless
  a period of 5 years has passed since the end of the sentence.

If you do not fall into one of these categories, then this section of the rules is not applicable and you would not get bounced all other things being equal. If you are asked about your history and lie about it, then other sections of Part 9 kick in which could lead to an adverse result for you. If charges are still pending, then failure to make a statement will make you an illegal entrant; you wrote that you were acquitted so this is also not applicable.

Additionally, and in a much more generic sense, Americans enter and visit the UK under Paragraph 23A of the rules, which says...

23A. A person who is not a visa national and who is seeking leave to enter on arrival in the United Kingdom for a period not exceeding 6 months for a purpose for which prior entry clearance is not required under these Rules may be granted such leave, for a period not exceeding 6 months.

That rule is subject to an examination by the Immigration Officer under paragraph 2A of Schedule 2 to the Immigration Act 1971, which we call a "landing interview". Sometimes they are brief and sometimes they are probing and invasive, and the outcome of a landing interview is down to your personal impact and articulation skills.

Also, notoriety (in itself) does not constitute grounds for removal from port as long as its nature does not affect public welfare.

So according to the rules and based upon what you wrote, your experience at the control point will be no different than any other American traveller.

Finally, British Immigration Officers are bound to reasonableness; they have to respect it. If a person demonstrates reasonable circumstances, they cannot do anything in the first instance. And (IMHO) it is not reasonable to waste time and resources on an innocent person.

With that being said, will I be able to get into UK?

Per UK law, all else being equal you should not be refused for having been merely accused. See Can a US citizen with a criminal record travel to the UK? by Gayot Fow (to whom thanks).

The UK Immigration Rules for Visitors state, in relevant part:

V 3.4 An application (except for an application for an extension of stay as a visitor) will be refused if the applicant has been convicted of a criminal offence for which they have been sentenced to a period of imprisonment of..........

and

V 3.5 An application will normally be refused if:

(a) within the period of 12 months before the application is decided, the applicant has been convicted of or admitted an offence for which they received a non-custodial sentence or out of court disposal that is recorded on their criminal record (except for an application for an extension of stay as a visitor); or.......

According to you, you were neither convicted nor admitted anything nor sentenced and hence you don't fall afoul of this. Be aware though, that when you visit the UK, you might be delayed at immigration for an extended interview depending on what information UK and USA shared if any on you. People can find this very stressful, but just try to relax and play it straight.

Do not volunteer this information to the immigration officer at the border unless you are prodded in some way, e.g have you ever had any problems with law enforcement. Such questions can be traps because although you were not convicted, you did have a brush with the law and denying can be grounds to be refused entry.