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OK chaps and chapesses, thinking caps on.

Talking to my financial advisors this week, they pointed out that there are some excellent offers of short-term fixed rate and easy-access fixed rate bank accounts right now, with 4.5% to 5.5% interest rates, but these won't be on offer much longer (in the UK) as interest rates are expected to tumble real soon.

Assuming one had the odd thousand or two (or ten or fifty thousand - you know whom I'm talking to, yes you there reading this page) lying around earning nothing in a current a/c, and wanted to shift some to a savings account, how much should one leave in reserve for immediate access ? (Wife's new knee, £15,000 payable in advance, springs to mind...)
Is there a formula relating incoming and outgoings and posible emergencies...

My wife put £20k in a one year fixed saving account with NatWest at 5.36% two weeks ago. It's supposed to be untouchable but you can make a withdrawl at 30 days notice with a penalty of 30 days interest.

I've always based my emergency fund on the following factors
1) House - likely expense to get something important replaced. Might be roof, boiler, washing machine. Something you can't work around.
2) Transport - backup if main means fails / becomes unavailable
3) Family - who might ask for what?
4) Employment change - probably not an issue now - replace with Medical as you allude to.

I have also thought about 5) Bargain. If something you've had your eye on suddenly becomes available cheap, you need the funds available.

I doubt my circumstances are anything like most others - I do all house repairs myself, for example - so I won't suggest a number for the actual value of the fund.

How you split this down into cash and short notice account depends on the possibilities of the negative events happening and the kind of short notice accounts one has access to.
My Credit Union is currently paying 3.8% for an instant access savings account, so outside of my immediate cash requirements I tend to dump a fair bit in there.
Living in Canada, it can happen that all the digital stuff, like credit cards and cash machines, become unavailable for at least 48 hours and possibly longer, so a decent wad of cash is a good idea.
However, we also have zero burglaries.

Final decision on pocket money: roughly £5,000 in each of four different instant access accounts, two with banks open at weekends. That's for daily use and emergencies.

Sounds about right - all the "experts" that I have read reckon about 6 months salary, that would be half my pension. Since I retired I have been putting into a separate account (called "Medical Accrual", but it can be used for any emergency) the same monthly amount as my last medical insurance (which had gone up ridiculously with increasing age). It now stands at £25K, enough to cover most things that I regard as an emergency but the NHS don't. I can instantly transfer it to any other account online.

BTW My local private hospital now offers interest-free terms on private work and you can pay the deposit on a credit card - I intend to utilise that if I need treatment.

I would keep one of those as cash, the size of notes that will be accepted anywhere.
Canada has lost all forms of electronic transactions a couple of times in the last three years, sometimes for over a day, including all ATMs.
Power cuts will have local effects, and the systems are getting worse, not better.

After the expletive deleted staff at RBS Guernsey blocked my card/app/internet banking on Friday (and they don't work Saturdays or Sundays of course) I decided 24hr access to a 'small' amount of my cash was vital. I now have four bank accounts with cash in them. Call me old-fashioned, possums, but life without instant funds is difficult.

I'm a great believer in cash, but it's not always 100% effective. A few years ago a large part of Sydney lost power. We lost it for 3 days, some lost it for more, due to a huge storm that bought trees down on multiple power lines. Of course, most businesses couldn't handle card transactions...but many couldn't get their cash registers open either. Of course, the little, flexible ones did OK.

Ho ho ho. Just went to the post office in Kingston. Closed due to power failure !

I say it, it happens.

It's a kind of magic

The emergency vet where we took Juno has signs up saying they don't take cash. I'm guessing part of that is for their own safety, if they're open 24hrs, they could otherwise have significant cash on the premises and unlocked doors at 3am.

We are not rich, but really rich enough. I am sure we could have done much better over the years but really chasing the dollars did not interest me and a couple of times when we tried to do better it all turned to custard. So here we are, retired, pensions almost twice our normal outgoings, new house built for us and money just sitting in the bank enough to build another.