Mid air refuelling for the Battle of Britain. Hmm. First thought, over the channel, in reach of British radar and fighter sweeps? How much fun would be being bounced while in mid- refuelling not be?
The only feasibly safe place is over home base- the 109's spiral up to operational altitude and then fill up, replacing the fuel they burnt off on the climb and leaving them with full tanks at thirty thousand feet.
I have only a vague idea how much of its' total nine hundred pound(ish) fuel load an E series 109 would use climbing to that height- a frighteningly large fraction, but details? At any rate, nearest round number, you're looking at two He111 based tankers per staffel- one could do it but you'd need the redundancy for malfunctions and cockups.
If my wild guess of about a third of fuel used to reach altitude is correct, you could be looking at escorted strikes as far inland as the rough arc Ipswich- Cambridge-Oxford-Portsmouth; how much does this really get you, when bombers are already scarce enough?
The one thing it does do is deprive Dowding of the option of retreat; there isn't a safe zone north of London any more. Which he never needed to do anyway, but...
It does make intruder operations later in the war nastily more practical, though- enough to tip the doctrine?
And yes, I was wrongly optimistic about the in service dates of the B-29. Complicated beast, that- adding in flight refuelling would only make it worse, too.