Sounds a wonderful start Stewart
Would be a good idea to have a meeting with the estate agent and get to understand what that letter means in terms of legal liabilities etc and also to discuss dates and conditions etc.
Usually the date of their entry is dependent upon the money being deposited to your account and confirmed by the bank.
DO NOT allow them to move in before that. Period.
Honestly Stewart, if you happy with the price and can live with their planned moving-in date then personally I wouldn't be too tough in any negotiations over the smaller issues. Sound like they have the money signed-off and also there's no chain. All good signs.
Someone's looking out for you
