I think you live in the UK??
As I understand it, you can buy whatever you please when you visit the USA and bring it back, except that there are certain foodstuffs you can't bring, you can't bring firearms, etc. I don't think that musical instruments fit into those categories unless they're made from the skin of endangered species. If you bring in excess of 145 UK pound worth of goods, you should declare it at UK customs and you'll have to pay tax on it. If you don't, you're breaking the UK law.
There are exceptions to this tax policy - if you're in the process of moving across and are bringing your used household goods (over 6 months old) , there's a dispensation, for example. But on the general rule of things, I don't believe that you qualify for a limitless taxfree allowance because you're a US citizen ... which I think is what you were hoping for?
Have a look around at
http://www.hmce.gov.uk for more details. Remember that the USA is not an EU country, so the UK has reciprocal tax arrangements described for the EU do NOT apply.