What’s been on my mind?

I’ve been wondering: Is there a constant C such that when your purchase costs any amount more than £C, and you go to the self-check out and deposit any amount of British coins, the weight of coins you receive as change is always less than the weight of the coins you paid with?

(Assume that the machine always spits out the as many large value coins as possible, e.g. it prefers to give one £2 coin rather than two £1 coins, etc.)

I have no idea what the answer is. :/