You can't shop tax free unless you're departing the UK/EU. You should just buy the pochette at LV in the city and then get VAT back at the airport later.
Here are my configurations GBP to USD on the bags I'm interested in (today's rate):
Alma MM vernis - 1580GBP (2810 on US site, 2439.75USD conversion from UK site price) (1311.40GBP minus VAT, 2024.99USD conversion). $785.01 savings.
Alma PM vernis - 1330GBP (2350 on US site, 2053.71USD conversion from UK site price) (1103.90GBP minus VAT, 1704.58USD conversion). $645.42 savings.
Neverfull MM Epi - 1160GBP (2050 on US site, 1791.21 conversion from UK site price) (962.80GBP minus VAT, 1486.70 conversion). $563.30 savings.
Bastille MM - 1670GBP (2960 on US site, 2578.72 conversion from UK site price) (1386.10GBP minus VAT, 2140.48 conversion). $819.52 savings.
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