I recently looked into parcel delivery from the UK to Ukraine and found a service that seems quite practical for people who prefer arranging shipments online. With Meest, you don't have to work out every detail at a physical branch first. You can enter the parcel information, check the estimated price and prepare the necessary details through the website.
I also like that there is a choice between air and ground delivery. Depending on what you're sending and how quickly you need it delivered, you can compare the available options before making a decision. There are different ways to hand over the parcel too, including drop-off locations and home collection.
For anyone who wants to check the conditions or calculate the price, here's the page explaining how to send parcel to Ukraine with Meest UK. It also covers parcel requirements, insurance and other useful details.