Trying to find where he was that day, I think I have an autograph of his and this date is typed next to it Alistair
According to Hansard In Parliament 22rd April 1943 then back in again 4th May 1943 A number of telegrams sent on 28th April 1943 Winston S. Churchill: Road to Victory, 1941–1945
The only mention in Alanbrooke is "Archie Wavell dining with PM" and then on 29th April : "...Portal informed me that PM last night had decided to start with Chiefs of Staff for Washington on Wednesday next...." So Churchill certainly seems to have been in London in the evening at least.
According to the Churchill Archives For Schools website, he sent a paper to the War Cabinet on 28th April 1943. Where he was when he did this I don't know though. Source: Churchill Archives For Schools
Images of the signature attached - this was tucked in the back of an RASC lads paybook that I've had for maybe 20 years - looking online a full autograph seems normal but there are a few with just initials, no reason to think this isn't right, from memory it wasn't mentioned when I bought the book, I'm sure if it was I'd remember or at the very least be aware I had it. Alistair
The 4th example on this webpage shows another example in red dated for 1940: Churchill Initials Looks good to me.
Old thread, I know, but posting for reference: Winston Churchill Appointment Diaries, Sept 1939 - June 1945