I have 300K to invest for 3 months - what's the best deal?

Would suggest that chasing the best return for such a short period may cause more problems than it is worth.
You will find delays in opening the account, losing 3 or more days interest moving the money from A to B and then back to A again, actually moving that sort of sum can be a problem as a lot of accounts have ?5,000 or ?10,000 daily transfer limits, the best rates tend to be with online accounts or obscure institutions, some accounts can take a week or more to open, need a chq to be sent to open, etc, etc.
Best advice i could offer would be to contact your own bank or building society, explain the situation and see what they have to offer before looking elsewhere. The big banks all offer the sort of account you are looking for and would be able to move your money between accounts at very short notice. You may be able to gain an extra 0.25% by going elsewhere but at what cost.
I was caught in exactly the same situation a few years back when i tried to earn an extra few quid on ?250k prior to a house purchase. Trying to get the cash back for the day we exchanged was an absolute nightmare, never again.