Hello, solicitor here.
On exchange, usually the buyer will pay to (or give to their solicitor) 10% of the purchase price of the property they are buying. This is Deposit, with a capital D. It's a contractual term being that should you change your mind and renege on the contract after exchange but before completion, you forfeit this sum.
When there's a chain involved, usually the deposit travels up the chain - so if you are selling for £120K, you get £12K in deposit from your sellers (you never GET this, really, but stay with me) and if you are buying for £200K your sellers' solicitor will either accept that £12K deposit (which doesn't usually actually travel, it's just "held to order" somewhere in the chain) or you might be asked to pony up a little more to get as close to that 10% Deposit as you can.
When all is said and done, your solicitor will figure out exactly how much you are owed from your sale, sweep that over to your purchase and then figure out exactly how much you are owed. You will usually get that money same day (i.e. completion date - moving day) unless completion happens really late but generally, it's a same day thing.
If all your money is tied up in the house, i.e. not available until you actually sell it, then you might have to do either a simultaneous exchange and completion (same day for both, not recommended) or find out as early as possible what you will receive as Deposit on your sale, press them to find more to get it to the 10% if you have to, and then either ask your sellers if they'll accept a reduced deposit (90% will say yes, if reasonable figure being talked about) or find that money somehow. Beware - if "finding the money somehow" your solicitor will have to ask you to account for every £, ID every party contributing and your new mortgage lender will have requirements re: other people putting funds into your house in terms of the money YOU put in (people also call this "deposit" funds when it isn't really - perhaps "deposit with a small d"!).
Best of luck - try not to worry, it all works out in the end. Don't overthink it.
TCT.