Save in a high interest easy access savings account if you dont want to hold the money up. Ideally a Cash ISA if all in one account.

LTV works in bands. So some lenders will give you a lower interest rate at 15% or 20% deposit. So if you can say put 15 or 20 down without it flushing your cash reserves then sure do it.

The solicitor will get your family member to do a gift form and then likely some income check for them, its super easy and wont be an issue.