bike parts get something like 4% duty (full bikes more IIRC), then there’s 20% VAT on top of that, and usually a handling charge from the courier.
Some brands wont ship US to Europe (see CRC/wiggle thread), most wont have warranty support (not used the importer so you’d have to go back to the US retailer with any issues, can you afford to ship a frame back to the US, or risk effectively having no warranty in which case why not buy second hand?).
Most reputable shops wont mark as gift on the grounds they are not willing to assist or conspire to evade taxes.
If you have a look at HMRC web site it is all there (or use search function, US imports been discussed many times and someone may have posted a direct link).
Not saying don’t do it, Ive bought loads of stuff from the US including forks for less than used prices here, but its not always cost effective.
edit, typed that at same time as everyone else 🙄 🙂