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Different Kinds of Diversification

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.

Practicalities

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 S&P 500 equivalent 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.

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.