Shipping carrier selection at checkout

[AlexanderWeb]

I have a Basic Shopify plan and I am using the Storefront API to build my own UI.

I am using the checkout url generated from GraphQl , I would like on the checkout to let a customer to choose a delivery option, something like the following. Most importantly I would like the pickup and shipping to be handled by a third party like DPD as we are only selling in the UK. At the moment as a postcode is entered a delivery fee of 5.99 is automatically pre-selected and I need to handle the shipping myself which is time consuming.

Can it be done? Thanks