If its not too late, HSBC have ATMs that can "read" cash and it's credited to your account immediately. I'm not sure where in Central London they have one that will be accessible, but there are ones at Canary Wharf and Stratford that are "open" (ie no staff working, but you can access the machines).

Just a cautionary tale, I had cash get jammed in these machines, once in the note reader and once in the coin machine. I was depositing notes on a Friday evening and there was nothing that could be done until Monday morning. Thankfully it was all fine and they called to confirmed it was in the account.