US citizenship is extremely valuable and your career opportunities at this stage are likely to be far more valuable to you in future earnings expectations than a few additional  percentage points on investments. 

In terms of investing, my understanding is that you are best off investing in the US and that there are US investment options open to you (Charles Schwab I believe often comes up as a broker in this area) rather than in the UK. 

I renounced my US citizenship two years ago (I still have a German one, living in Germany) because of the restrictions on opening bank accounts, the uncertainty on taxes on capital gains as well around inheritance taxes as well as the yearly cost of paying and additional CPA for the US return. The process was pretty straight forward (going to the consulate, paying the exit fee) and at that time they told me at the consulate that many people were doing this.I've since then travelled to the US once and wasn't questioned at the border.

Not having the option to work in the US is a significant downside so I wouldn't take the decision lightly. However once you start having more assets outside the US (especially if you start investing in companies) the risks and tax requirements can be significant.

If you can manage to open a bank account in the US it might be easier to invest there but usually you need a permanent address.

I short I think it's worthwhile to invest some time (and perhaps money in advisors) in further researching the options you have before making a decision that either reduces your work options or exposes you to unknown financial risks.

Do you currently have significant assets? I am not an expert in this but historically the US has imposed exit taxes on people who renounce their citizenship, to try to recoup the taxes they think you 'should' have paid.

I'm not very familiar with investment options in the UK, but there are of course many investment options in the US. I believe that being a citizen of the US helps a fair bit for some of these options. 

My impression is that getting full citizenship of both the US and the UK is generally extremely difficult, I imagine ever changing your mind would be quite a challenge.

One really nice benefit of having both citizenship is that it gives you a lot of flexibility. If either country suddenly becomes much more preferable for some reason or another (imagine some tail risk, like a political disaster of some sort), you have the option of easily going to the other. 

You also need account for how the US might treat you if you do renounce citizenship. My impression is that they can be quite unfavorable to those who do this (particularly if they think it's for tax reasons); both by coming at these people for assets, making it difficult to come back to the US for any reason, or other things. 

I would be very hesitant to renounce citizenship of either, until you really do a fair amount of research on the cons of the matter.

https://foreignpolicy.com/2012/05/17/could-eduardo-saverin-be-barred-from-the-u-s-for-life/