You’ll be fine from that base level of fitness, just make sure you get some back to back long days in the lead up to it.
I did it in 8 days this September – total distance 1014 miles. I’d not ridden 100 miles on the road before and never done back to back century days.
Far from ideal preparation for most people, but I have a good level of fitness from fell racing and adventure racing through the summer. I’d only just finished a 4 day adventure race 5 days before I set off on LEJOG!
Had a few minor niggles towards the end mainly a sore neck, so I’d definitely recommend doing some other conditioning work off the bike.
The main things are really make sure you are comfortable on the bike, try and keep weight to a minimum to make and most of all enjoy it. Its a great way to see the country.