Hi Charlie,
A few years ago at the end of April / beginning of May - ran the London Marathon (2:59) then 4 days later cycled from Land's End to John O'Groats in 10 days then the day after ran the Silverstone 10k in 37 minutes. So I'd say it's very much possible!
I began training in February as I'd been off running a couple of months with injury. I'd cross trained in the meantime. Once I was able to start running I focused more on training for the marathon than the cycling, aiming to get out once a week or so for a minimum 60 mile bike ride. I was relying on the cycling fitness compensating for lack of saddle time.
The marathon went better than expected, the LEJOG was hard work - especially in the first few days as I hadn't fully recovered from the marathon, but after a few days I found my cycling legs and found that all the running helped loads on the hills in Scotland.
To be honest, your two events are months apart, so you could concentrate on the cycling up till June then after a week or so rest prioritise on training for a marathon. Once you've shaken the fatigue out of your legs you'll hopefully feel fitter for all the cycling - and those two hour plus long runs will feel like nothing after 9 long days in the saddle!
You could keep up with some running whilst training with cycling - I think that all but the most dedicated cyclists can benefit from some running incorporated around the bike rides.
Good luck!