Just to confirm, either party can pull out at any time until exchange of contracts. So advisable not to exchange until you have found somewhere, if buying and selling it is usual to tie the two in so they exchange and complete together.
You are not legally bound to complete the purchase until exchange of contracts.
The completion date is set then and written into the contract and you are contractually bound to complete on that date. If you do not there are a number of remedies that can be used. Interest can be charged at the contract rate (usually 4/5% above the base rate of a certain bank so can be around 9/10%) of the full purchase price per day you don't complete, including weekends.
If the other party is ready, willing and able to complete they can serve notice to complete can also be served giving usually 10 working days to complete or the other party can rescind (pull out) of the contract and keep the deposit. Even if less than the usual 10% was paid they are entitled to the full 10%.
A notice fee would also be payable as specified in the contract, can be �75-125.00 plus VAT which you would be liable for.
Exchange and completion can take place simultaneously on the same day if required, unlikely if there is a chain though.
As said above, a significant delay may cause problems especially if a chain is involved and there is a danger of the chain collapsing. It depends on the buyer's circumstances, even if they have no related sale they may need to give notice for rental accomodation or may be relocating so will have to sort out employment issues, removals and other issues.
Proably best to find somewhere or have the circumstances made clear to a purchaser. Speak to the agents.