The main issue you'll have is dealing with taxation; the UK bank will possibly deduct tax off any interest paid. However as a legal permanent alien you'll be required to inform the IRS of the interest accrued and, in the process, avoid paying a double taxation hit using the tax treaties in effect between the UK & the US.

I tried it a few years ago and was eventually hit by AMT (Alternative Minimum Tax) as a result of it (which raised my ire somewhat) so I eventually gave up. Whilst not having a pound sterling account has been somewhat of an inconvenience (paying for my British magazine subscriptions) by and large I've been able to work around it and have a more peaceful life as a result - however circumstances differ between folk so it's probably worth keeping it open for a while and see how you go.

As Fatbrit mentioned earlier though - it's a darned site harder to open a UK account as an expat so do think carefully before making that closure decision.