I've read Joy Larkcoms book cover to cover, which suggest I may have
to wait two season before I can plant anything.

Not having read the book I'm not sure what the idea is here. But I
doubt you need to wait. Even if there is some kind of soil-building
or weed-killing plan which takes time, you can always save a small
plot as the "immediate (well, short-term) gratification area".

Being as impatient as I am, does anyone have any suggestions as to what
I can put in it in the next six weeks or so to get it going, or should I
leave it until next spring?

My first thought is some kind of cover crop. Maybe a legume (such as
clover) to fix nitrogen. This will help shade and out-compete weeds,
and you can till it in (or trim and put in the compost, if you are of
the no-till philosophy) in the spring. This also buys you time to
think while you are figuring out what to plant.

You can probably grow a lot of cool weather crops this fall too
(broccoli, cabbage, lettuce, maybe carrots, spinach, probably others
I'm not thinking of just now). If you are indeed in the UK, and I
understand the UK climate right, the winters are mild so these should
grow well into the fall, and kind of gradually slow down rather than
get nailed by a lot of snow, heavy frost, etc. The sooner you start
on these, the more chance of a harvest. Just planted my fall broccoli
here in Washington, DC (a climate with hotter summers and colder
winters, but also northern hemisphere). My first year trying this
plant (and planting timing), so no firsthand knowledge yet about
whether I am doing this right.