Cheapest transaction fees for buying and sending BTC? (UK)

I purchased BTC on Coinbase this morning. £70 incurred a 4% charge for transaction fee. When I sent it to cold storage, it cost me £10 (14% of the initial amount) and I genuinely feel I’ve been molested lol.

What’s the best ‘middleman’ when it comes to the lowest fees? I’m not looking to hold any of my BTC on an exchange, as I send it to cold storage instantaneously.

Cheers in advance.