Try some "shake-down" weekend trips this year, and you'll figure out what works and what's worth upgrading.
Look on maps.google.com and push the bicycle button for suggested bike routes to Dover.
Join warmshowers.com for possible hosts on your route, too.
I would not enjoy touring on a mountain bike or with those tires, but plenty do.
I just finished a long tour (7100 km) in the States and spend less than US$25 per day, and I'm an old guy with a credit card. You might do OK on 20 Euros. Don't eat at restaurants and camp a lot.