Back in US - Can I get a VAT Refund

I don't think so. You need to have a form identifying the merchandise you purchased and took out of the country unused; signed by a Customs agent at the airport of departure.

They had to see the items and the proper forms at the border, Heathrow Airport in this case, to prove they were leaving the country. Sorry! VAT refund isn't for services, hotels, meals, etc anyway.

The logic in granting a VAT refund is that the items are leaving the country and not used/consumed in the EU. You need to demonstrate that the merchandise is leaving the EU.

A number of years ago we bought wool sweaters in Norway. The store had to seal the sweaters in a bag to guarantee that they weren't used in Norway.

You probably inadvertently asked the question in a manner that was misinterpreted - giving you a VAT number sounds more like what you would use in connection with VAT returns as a local business.

You needed to ask about 'Tax Free Shopping'. If the shop doesn't operate the scheme then there is no mechanism for a VAT refund (on legitimately exported items).

As you see above, you won't be able to get any back, and as said because you can't prove that what you took out of the EU was new and unused.

If you have used it - hotels, meals, clothing you bought and wore, electronics including phones you bought and used, tickets, taxi fares, etc., - you can't claim and would never have received a rebate on.

I hope you had a good time even paying the VAT which was inside the prices you paid.

No, you cannot.

Besides you wouldn't have been eligible for the VAT on most if not all of those purchases anyway.

It's usually only if you spend a whole huge hunk of money in one store - on things that you're exporting from the EU. Little bits and pieces, things you used or consumed there, etc etc, aren't eligible for VAT refund. People visiting the United States don't get to ask for their sales tax money back.

Some states do have a rebate scheme on sales tax for visitors - but again it is for big-ish ticket export items, not day to day tourist expenditure.

Example of sales tax exemption in the States:
http://dor.wa.gov/Content/FindTaxesAndRates/RetailSalesTax/Nonresidents/default.aspx

A sales tax exemption exists for certain nonresidents of Washington
State on purchases of tangible personal property, digital goods, and
digital codes, that will be used only outside of this state. This
exemption is only available to residents of states, United States
possessions, or Canadian provinces where: There is no retail sales
tax, use tax, value added tax....

And I am wondering how many out there after actually claiming a VAT refund are then reporting their purchases to their state of residence on their state income tax return and paying their state the required sales tax on purchases of goods brought in but made out of state (with no or reduced sales tax) or online without sales tax? I would believe this is a requirement in all states that have a sales and income tax, but I would have to look it up to be sure; I can report from working with their income tax forms that this is required in PA, NJ, and VT. And if you have not kept direct records, there is a table to calculate your expected purchase amount and the sales tax due based on your reported taxable income (which in PA is totally unrealistic as neither our pensions, our Social Security, nor our tax-free interest count as income in PA)

...reporting their purchases to their state of residence on their state income tax return and paying their state the required sales tax on purchases of goods brought in but made out of state (with no or reduced sales tax) or online without sales tax?

I've been told by State of Washington colleagues that Washington businesses that make purchases in Oregon (no sales tax) must remit Washington sales taxes on their Oregon purchases. In suppose remitting the WA tax is more than offset by expensing or depreciating their OR purchase.

Maybe I should have added the complicating factor - Delaware has no sales tax, and it is common for people to drive there from PA and NJ to purchase large ticket items for their own personal use, saving 6% (or 8% if they live in Philadelphia). The home states want the sales tax that was thus ducked, just like with internet purchases where the seller does not have any physical presence in the state and thus is not required to collect the local sales tax for the delivery address. And, to be technical, you are not allowed to even think about buying alcohol outside PA and bringing it back across the border, which is not just a tax issue, it's a matter of PA has a horrible state-run monopoly on spirits. People have been known to have their cars intercepted at the border, fined, and relieved of their purchases.

the way I am reading your post you are looking to claim back vat on everything you spent in the Uk including the vat on meals .This is not allowed.
You can only claim back VAT on unused items you are taking out of the country and nothing else. you cannot claim back vat o.n meals accommodation etc.
You must claim the vat back at the last place you are leaving the EU .You have no chance of claiming any VAT back now you are back home.