On average, a UPS package is going to set you back a minimum of around $70 USD to the UK. And that's without declaring a high value and marking it as a gift, and before import taxes and anything else you might get charged on that end.
That's what it usually costs me to send a small box or padded envelope through work, and we get reduced rates.
USPS you could maybe get something small with a brake or derailleur etc, for $20-30? But don't quote me on that, because I never go to the post office!
And as the above says, it'll probably take a couple of weeks at least. UPS with be within 5 business days.