You should get your solicitor to confirm all these numbers, but here is my summary.
The seller will expect a deposit of approx 10% on signing the contract, but the mortgage money will not have been paid out by then. You need to fund this yourself.
So, the numbers look something like this
First, you pay out 2K EA deposit ( my guess)
On signing contracts, the seller wants a deposit of 22.5K. You must pay this in cash, through your solicitor.
I think the EA passes their deposit to the solicitor on signing, to make up part of this deposit but you should confirm this. If not, you need to have 22.5K in cash, for the deposit.
When the sale completes, the solicitor will get a mortgage cheque for 207K. He will pay the seller the remaining 202.5K, take his fee and return the rest to you.
If you can't cover the full 10% deposit, in advance of getting the mortgage cheque, you can ask if an 8% deposit is acceptable.