Part of the answer depends on your domicile and residence. For example, an American who moved to the UK and acquired British citizenship may have a different answer than a Brit who moved to American, acquired US citizenship, and then returned to the UK.
Generally, the treaty says that you are to be taxed on pensions first in your country of residence. If the pension is from the non-residence country, it may be allowed the same tax breaks in the residence country.
An IRA and a 401k are generally taxed in the US as income, though some 401k distributions can be taxed as capital gains. If it is a regular IRA/401k, it is taxed upon taking it out. If it is a Roth IRA/401k, it can be tax-free when you take it out, if you take it out under the right circumstances. That same taxable or tax-free status would also be allowed in the UK.
You will also have to report the income on your US return. You can take a deduction for any UK tax paid, using a treaty claim.
If the treaty is not applicable in your situation, then the US taxes the income and it's the UK that gives a tax credit for the US taxes paid. You may also be exempt from tax on the pension in the UK if you do not remit the funds to the UK. All these questions depend on personal circumstances regarding domicile, residence, and citizenship.
As your personal circumstances determine whether the US or the UK has the first "bite" of taxes, you should consider speaking with a qualified UK tax expert to see whether the treaty applies in your case; ideally you should also arrange for co-ordinated US advice.