I believe that as a freelancer, I need to register in the UK upon arrival in order to help when tax time rolls around.
If you are self-employed, then yes, after arriving in the UK you will need to register the existence of your business with HMRC .... Her Majesty's Revenue & Customs .... within 3 months. Failure to do so might result in a £100 penalty being levied .
Registering the business will not just notify the matter from the tax point of view, but also as regards NICs .... National Insurance Contributions. If you are self-employed then you will be liable for Class 2 contributions, but it is easy to set up a Direct Debit to pay those automatically each month.
Also VAT! Value Added Tax? Might you be liable to register for that? It depends upon the turnover of your business. Are you able to tell us roughly how much turnover we are talking about?
Alternatively, instead of you being self-employed, you might set up a UK limited company, there then being a contract between the US company and your own company. In this case you would not be self-employed, but would be paid as a Director of the company, and take dividend income from it. Dependent upon the size of the figures, this might save you a sizeable chunk of UK tax.
However, I am aware from topics in this section of this Board that if you do set up your own limited company, then under US tax law it would be a CFC .... Controlled Foreign Corporation ..... and you would need to fully consider the implications of that.
Also appreciate that unless you form your own limited company, it is possible that unless HMRC see your business as a genuine business, they might not agree that you are self-employed. The point is this. If you were employed in the UK then employer's NICs would be payable. In other words, there might be a tax risk, or rather NIC risk, that HMRC might try to collect employer's NICs.
Your business .... would it be a one-client business? Or would there also be other clients? Possibly from the UK? Not necessarily immediately, but might other clients get added later?
But hey, you are just about to get married! You don't want to cloud your mind now with the finer details of your situation after you arrive in the UK!