I reckon it is unusual but really it is not unreasonable. If you have planned for this outlay in your budget then it should not be a problem. Anyway i think a solicitor has some kind of lien on your property until the fees are paid.
You oughn't to pick a solicitor just because it's the lowest fee.
As you are not a client there is nothing wrong with requesting part of the fee up front. Be sure to get a S68 letter. It's your legal entitlement. Do you understand the difference between fee and outlays ? Also ask what happens if the sale does not go thru. How much is the fee?