If I invest £2,000 in bitcoin and the price goes down, can I lose more than my investment. Could i Have to sell my house to pay back the losses? If I invest in Bitcoin is it possible to lose more than my initial investment ?
In other words if the price goes down substantially, to well below that of when I initially invested; is it possible that I might be sent a bill for the further losses ? Could I be sued for Bitcoin losses ?
I might be prepared to risk an investment if all I can lose is that investment, however I may not be prepared to make an investment if there is a risk, however seemingly small at the moment, that Bitcoin investors may be sued or expected to sell their house to pay off Bitcoin debts in the future.
...if the price goes down substantially, to well below that of when I initially invested; is it possible that I might be sent a bill for the further losses ?


No. 

If the price of a bitcoin dropped to $0, you would lose your entire investment, but no more than that. 

Think of it like buying gold: if the price of gold dropped to zero, you would now just own some worthless metal. You wouldn't owe anyone money, you would simply have lost the capital you used to buy the gold in the first place. 

The only way you are going to owe more money than your investment is through some external factor. As an example, if you took out a loan to buy bitcoin, and then owed interest on the loan. But that debt would be owed to whoever lent you the money.