Different Kinds of Diversification
There's not a "optimum" diversification that one can select - diversification protects against specific kinds of risks, and therefore depends on your risk assessment.
You can diversify by owning different stocks within the same sector. You are protected from the risk of - say - the Volkswagen emissions scandal by purchasing other auto makers.
But what if the auto industry as a whole declines? You may invest in a broader array a stocks - say by purchasing shares of an S&P 500 index - to protect against a decline in one sector.
But the S&P 500 is a group of American stocks - there is a risk that the American economy will decline. You can mitigate that risk by investing in other countries' companies.
But the US economy is one of the faster growing economies in the world, and you're protected from the risks of investing in potentially volatile developing economies. So the balance you select in a "total world" portfolio is really your assessment of what countries you think are going to grow their economies best in over the time period you are investing. There's not consensus to be had on that answer, because no one knows!
Two major things you should look into are: Fees and taxes.
In the US a fee of ~ 1% is high for an index fund, and a fee around ~0.15% is probably reasonable. Fees may differ depending on how much you invest, what kind of work goes into creating the index, etc.
You may also face additional taxes or fees for investing in foreign stocks. This will be very location dependent.
Anything More Specific Depends on You##
It is difficult to give good advice on diversification that is specific to your position. It's mostly a matter of your risk tolerance, and risk assessment.
If you are confident in the UK economy, find a UK equivalent of the S&P 500 and don't worry about it.
If you're worried about the UK economy - say because Brexit makes you nervous - then look for more international funds. Again, which countries you choose to invest in and in what ratios depends heavily on how you think those economies will perform over time.
I'd shop around on different brokerage websites. They will provide a breakdown of holdings for each fund - x% large companies, y% small companies, p% local, q% international, etc. Find combination of funds that make you feel confident and has low fees.