I'm probably not the best person to answer this, since I am not an avid cyclist and I live in flat Florida, although we DO have bridges, which race directors think is a good idea to add into every triathlon. I do what TucsonJill describes - keep a constant cadence but start dropping the gears as it starts getting difficult to pedal, while powering from your hips rather than your quads. I have passed many people up bridges in triathlons using this method, and rarely have to stand up. Just before you crest the hill, start gearing back up, because once you hit the top and start the downhill you will want that pedal control.
You say you are a masher, and that may make hills more difficult because 1) mashing using more energy, and 2) your power is coming from your legs. If you want to get past the mashing, learn correct spinning technique. You can find You Tube videos that show this and I'm sure there are books and websites that explain it.
One day I would love to get back over to Wales and do some cycling. It's a beautiful country!
"God gave you your body as a gift, so you should take care of it." - My Mom