I'm a 56 year old non-resident alien living in the United Kingdom with an income from rental property in the US of about $30,000 per year. I do not need additional income at this time so what are the advantages and disadvantages of putting the money into an IRA or other pension scheme? And which should I choose?

I don't see much of an advantage in doing this. You can not deduct the IRA contribution from your income for US tax purposes, since you have no earned income. So the only advangate is tax-deferral on the future earnings in the IRA. This might be worthwhile, if you're willing to deal with the paperwork.

As for which one - that's up to you. Some firms allow non-resident aliens to open IRA accounts, but many do not. You may want to check out Fidelity and Vanguard.