How can a noob understand 'where their money went' when buying from bittylicious? Complete newbie, trying out bitcoin for the first time (probably like everyone else in the world this morning).

Wanted to spend the maximum allowed for a new user - about 43 pounds.

When the full transaction details came up, I was being offered to buy 2.9 mBTC for this amount - at the bitcoin rate at the time, that was only about 33 dollars' worth of bitcoin - so, about 24 pounds! 

On the face of it, the transaction results in me losing half my money!
How can I tell where that money 'goes'? Is it a transaction fee, or am I somehow just paying a strange price?
From the transaction link provided (link)

You can see that fees was just below $2 for this transaction:



So the rest (about 18 pounds) have been taken as a commission/fees for using their interface.

I would suggest you to try some other website to buy BTC, as you are paying a very high fees to buy BTC.