An English pack won’t fit. Best bet is to sell several packs, pack them between card savers and slab sleeves, and ship them first class in a bubble mailer. Deep Pocket Monster has a YouTube video showing how you can store single packs.
Honestly, when buying from online sellers, I prefer the sellers not try to save a few pennies on shipping. Even if they pass the extra shipping costs on to me, at least it’s a sign that they care about the product they are sending me, and will give it the protection it deserves.
Please do not bend hardbacked envelopes with a card in a toploader fit as standard letters in the UK so maybe try that? that is how I send my singles, I can put 2 cards back to back in separate penny sleeves in a toploader.
use the ~.70 cent option instead of the ~.50 cent option. So set you envelope to 2oz even if it doesn’t actually weigh 2oz. This is because the .50 cent option means the envelope is machinable and the .70 cent option means it’s not. Running the envelope through the machine can damage the card.