There seem to be two questions here: first how to choose your desired percentage allocation, and secondly how to implement that in the UK. Answering the second first:
In the UK, this will depend heavily on the platform through which you are investing. If you are investing via a SIPP or ISA, you will generally be constrained to those funds that the provider has a deal with to provide at a reasonable price. Fees in general are eye-watering compared to the US, so it will be wise to constrain yourself to whichever fund providers are advantaged in that sense. All that I'm aware of will offer index funds from some provider, look for either "index" or "tracker" in the name of the fund.
If you are talking about a regular, taxed, brokerage account, you may be able to access US ETFs directly (though you may incur a paperwork burden by having to file US taxes in order to reclaim taxes withheld in the US).
It may be wise to first choose your intended geographic/sector/whatever breakdown by using tools on somewhere like ETFdb or Morningstar and then finding corresponding funds on your platform...
But if your question is actually how to choose the percentage weights of your desired allocation, that's advice for which you would be wise to seek a financial advisor. Just be aware that most equity markets are reasonably highly correlated most of the time, so minor differences in allocation weights are not going to make huge differences in your expected risk or return. Depending on whether you subscribe to Modern Portfolio Theory or not, you (read: "your advisor") could obtain the historical returns for your various ETFs and then construct the covariance matrix, using it to then find an "efficient portfolio" in some sense, then decide whether you wish to take active bets based on that efficient mix of assets. You will likely find, if you pursue this, that unless you use some relatively sophisticated statistical techniques (lookup "covariance shrinkage"), that your answers will vary wildly depending on exactly where you cut off your historical data... Whether this all becomes a bit of a fool's errand is ultimately up to you. You might find it more productive to figure some relatively simple global weights and then not worry too much about it!
What you should not do is allocate based on your confidence in the economy of a country or countries. Nobel laureates who do this for a living show a poor track record of gaging economies, you are unlikely to do better than them. Buying based on your confidence is exactly why people buy high and sell low. And in any case, even if you had a crystal ball and perfect discipline, economies and stock markets are only correlated in the very long term.
You may find articles like http://www.crainswealth.com/article/20161021/WEALTH/161029985/5-top-wall-street-investors-weigh-in-on-the-best-ways-to-invest helpful to formulate your own thinking, but again: formulating your desired portfolio allocation will be a different question to how to implement it, especially in the UK. And I said it before, but it bears repeating: watch out for fees!
None of this is financial advice and I am not your financial advisor... and I hesitate to recommend any specific product or platform, but since you mention a predilection for index funds, you may or may not know the story of Jack Bogle and Vanguard, who are reasonably famous for championing low cost index funds (since well before it was "cool"). You may be interested to know that Vanguard has a UK platform and you can apparently open an ISA with them.