It depends on the weight (and, I think, size) of your cards. There's no standard rate to the US. This is why you should ALWAYS buy the smallest, lightest cards possible to go overseas!
If you have an accurate scale (preferably digital), you can pay for postage online and print it out yourself from the Royal Mail website. This is pretty handy if you can't get to a post office.
Unfortunately mailing cards individually to the US is quite pricey. If you can have a friend or family member hand out cards or even willing to post them for yyou within the US you you may want to look at grouping them to sending them that way in a big padded envelope - sending like 20 cards in a padded envelope costs me approximately £2.50-5 to mail to the US as opposed to £1-1.50 per card to mail to the US.
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(Depending on the size & weight of cards being sent, as well as any other gifts I send over - usually calendars.)
Another option for future is you may want to invest in a good quantity of
Forever Stamps form the USPS and stamping all the letters and asking a friend or family member to mail the cards for you after you send them in bulk from the UK...
When you go to the post office to mail your letters you need to inform them that you have x amount of letters to send to the USA. They'll have you put each one on the scale and depending on weight will either give you stamps to lick and put on each card (which can end up being several of different amounts to equal the cost you need) or if over £1 they'll print out a sticker, but this will usually need to be done on every single card / letter.
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Good luck!