Can Coinbase Bitcoin network fee really be 50% Ive just bough £47.81 of bitcoin.  After fees i'm left with 0.00375837 BTC. 
I want to buy another cryptocurrency but the network fee is 0.00186539 so i'm left with only £24.41.

Can this fee be correct?  Thats close to 50%.  Is it the sum im trying to trade?
Transaction fees are calculated based upon the size of the tx in bytes, not the amount being transferred. Right now the network is very congested, so fees are higher than normal. In this case Coinbase is initiating the tx, so you are at their mercy to dictate the fee (that said, setting a lower fee may mean your tx does not confirm). If you trade within the coinbase exchange (not sending coins to another exchange), you should not be charged network tx fees.

Once the backlog of txs clears out, it will be cheaper to transact again.