Dodder is very common round here, mostly parasitising gorse. It never climbs very high. It smells horrible when in flower in August. Galium mollugo, hedge bedstraw, doesn't really climb high much either. Ladies' bedstraw is a definite ground-hugger. I mentioned goosegrass/cleavers/sticky willy, another bedstraw, not only because of the "bed" allusion in its name but also because it can climb rampantly a good number of feet up trees and shrubs.