Calculated UK shipping app

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We have just started shipping our products UK only. We ship furniture and homeware using UK couriers. 
We are currently shipping approx 30-50 orders a month.

We have manually entered weight based shipping rates. We have calculated these based on our product weight and rough estimates from couriers.
As these are only based on estimates there are a few mistakes and we end up not charging the correct amounts and occurring extra costs.

Also as we are shipping furniture courier costs can vary a lot depending on size which can vary greatly. Making things even harder to calculate.

We have started looking into the Shopify apps such as Better Shipping.

1. Is there an app we can download that will link with UK couriers (for small and large items) to calculate an accurate shipping rate at checkout? 

We are based in the south of England and are occurring extra charges when shipping to Scotland. 

2. Does anyone know how to manually add distance into your shipping fees? We can only find regions which includes all of the UK rather than distance from start point.