I think it might be difficult to get a UK bank account, actually. They are quite strict about proving your address and such, and restrictive of what sort of account they will give people. I am currently on a 1 year student visa and just haven't been able to get a good account. I am hoping that when I switch to a 2 year post study work visa that I will be able to get a better bank account.
If you are in the UK because you are stationed there you MIGHT be able to get one, but I think they might expect you to just go through the military banking system and might not be all that willing to let you open an account. The amount you have to deposit, unless it were REALLY a lot, probably wouldn't entice them much. I had a large initial deposit between savings and student loans and they seemed entirely unimpressed.
I doubt having the account in the UK would help as far as immigration. Having savings in the US in dollars will do you the same amount of good as having that money in the UK. Since you are making money in dollars at the moment I would think, you would have to be converting your currency every time you make a deposit, so with currency fluctuations it could help or hurt you in the long run. Of course no one knows what the dollar will be worth in 3 years, it might buy you more £s or less. It's always a gamble.
I would suggest just saving what you can so you can show substantial nest egg. But in the end, for immigration, they just like to see that you have savings so you won't end up on the street or needing financial support for which you will not be eligible. You'll still need to deal with either meeting the requirements for the Tier 1 Highly Skilled or Tier 2 sponsored worker visas, I would think.
Best,
Elizabeth