nun

The you would be breaking the law and you don't ever want the IRS coming after you. As a US resident you MUST declare your worldwide income!!!!!!

Your ISAs are not tax free in the US so you must declare all interest and gains on your 1040 so the IRS can tax it. If you have a cash ISA you declare the interest and file any FBAR or FATCA forms required. If you have a stocks and shares ISA you will have to file (Passive Foreign Investment Corporation) PFIC forms and foreign trust forms too. The PFICs are any foreign pooled investment like a UK unit trust, tracker fund etc. and are complicated and the tax rates are high so US residents and citizens are always told to avoid PFICs outside of certain retirement and insurance accounts "like the plague". So I would get rid of any Stocks and Shares ISAs asap.

What type of UK pensions do you have? and they SIPPs, personal pensions and final salary pensions. Some financial advisors will make a distinction between how these various pensions are dealt with for US tax purposes. The simplest approach is too claim a treaty exemption on any gains within all the pensions during the accumulation phase. This will insulate you from any PFIC issues. This is seen as an aggressive stance by some advisors. When you take income out you would file a US/Individual 2002 with the IRS who would send that to HMRC and your UK tax code on withdrawals will be changed by HMRC to NT. So you'd pay no UK tax but would have to pay US income tax.