Is there a way to request a UK adapter for my new iPad order?

Apple will only ship products that are intended for the country/region within which they are purchased. As such, devices purchased in the US will have a US-specification Power Adapter; similarly, a device purchased in the UK will have a UK-specification Power Adapter.

Be aware, however, that all Apple USB Power Adapters are designed for use with AC-power sources rated to provide 100VAC to 240VAC at 50Hz to 60Hz.  Apple iPad USB power adapters also comply with the IEC/UL 60950-1 and IEC/UL 62368-1 standards for use with power sources rated to provide 115VAC at 400Hz (typically found onboard commercial airlines).

While your US-sourced Power Adapter will be fully usable when travelling internationally, you may require a simple pin-adapter to allow the Power Adapter to be used with AC power outlets in different countries. For example, a US flat 2-pin connector will require an adapter for the standard European round 2-pin socket. Travel adapters are readily available.

Generally, although Apple provides an international one-year limited warranty for products, you should aim to purchase a device in the country within which you intend to spend most time - as this often simplifies the warranty position should you ever need to call upon it. Also consider that optional AppleCare+, if purchased, will only be valid/honoured within the country of purchase.

Not if you are ordering from the US store. You can wait until you get to the UK to order, or go to a store to pickup, or you can use get a UK adapter when you get there.