Can I buy a refurbished Macbook in the offline London Apple Store I'm about to travel to UK, and i'm wondering if I can buy a refurbished Macbook, straight from the Apple Store, not from the website.

I'm not a UK resident, and I would like to get a TAX refund, and it seems like the VAT TAX refund rules mention that the online sales are not eligible.

Is this possible?
In the United States you cannot buy a refurbished product and have it shipped for in-store pickup. Have you tried to see if you can do that through the UK online store? 

In general the retail stores stock a subset of all of the standard models in some cases they even stock custom build versions that are popular in that specific location. Also, refurbished products are so limited compared to the normal production that it all gets held at central shipping locations and you can only buy it online. I have heard of businesses ordering tens or dozens of Macs when there's enough inventory for refurbished products, but you would then be working with a business specialist in that case to work up your quote and they could answer all of your questions during the pre-sales discussion.

You could try looking up the contact information for the specific store you intended to shop: http://www.apple.com/retail/storelist/

My understanding, is that the stores are staffed to handle the people that walk in physically as opposed to field phone calls and email messages from potential shoppers. That being said, a polite email or short call might be worth your time to gather information about refurbished products in that specific market.

Either way, you should go visit the stores in London for I hear they are amazing to witness in person.