To put some numbers on it ... (using
Bike Calculator)
If you weigh 13 stone and your bike weighs 18 pounds, there is no wind, you are riding on the hoods and have properly inflated clincher tyres, then you would have to be able to generate about 106 Watts to cycle at 15 mph. Most people can ride at 15 mph in still conditions on a level road for at least 15 minutes.
Now plug 106 Watts into the same calculator with the gradient set to 10% and you get about 2.4 mph. That is a grovelling speed, sure enough, but it is possible to ride that slowly without falling off. (I know - I do it!)
If you try doing 2.4 mph in a 39/25 gear, your cadence would be uncomfortably low - just below 20 rpm. You could struggle to get the cranks through the dead spots in the pedal stroke, so ideally you need a much lower gear.
You definitely have the power to ride up the hill, if you go slowly enough, and in a low enough gear to get the cranks round.
Using those figures - it would take about 25 minutes to grovel up the Beacon!